I've always wanted to visit the Intergalactic Museum of Art and Natural History. Just think of what kind of a grand place it would be.
It'd be a pretty big place, of course. Intergalactic, that means it'd cover the art and natural history of more than one galaxy. Even tiny galaxies are big, containing millions of stars, perhaps thousands if not hundreds of thousands of civilizations, and certainly millions if not billions of planets each with their own natural history. There's no way you can fit all of that into a building. Even an ordinary planet wouldn't be big enough.
I imagine the entrance itself might look like a building though. It would be the result of an intergalactic competition of architects. Some if not most of the architects might not even know they're participating in a competition. After all, the people curating the museum wouldn't want to involve civilizations in the Intergalactic Commonwealth unless they were ready. (We have to assume there's an Intergalactic Commonwealth, because who else would build the Intergalactic Museum. And we have to assume that the Intergalactic Commonwealth doesn't contact cultures that are not ready to join because, after all, we haven't been contacted, yet.)
So this competition would itself take a considerable amount of time, of course. Maybe not millions or billions of years (the time for light to travel from one galaxy to the next), but even if some kind of faster than light transmission of information were possible, it'd be a while before the hundreds of thousands of entries to the competition were collected. There'd be a committee, comprised of members from several representative cultures, to select the finalists based on criteria of scientific aesthetics. (Scientific aesthetics is what you get when you figure out why things are pleasing and interesting, and generalize it enough so that creatures from a wide variety of cultures will appreciate it.)
In fact, now that I think about it, it's entirely possible that there may be many modes of aesthetic perception, each the result of the evolution of various creatures. I don't expect there to be an infinite variety of modes, since the cultures that would be considered for this project would all have certain things in common, but there'd likely be more than one. Perhaps hundreds, or even thousands. In fact, there might be a committee established for each of these modes, and each would select their own winners.
Eventually the entrances to the Intergalactic Museum of Art and Natural History would be built. If an entire planet isn't large enough - I figure they'd perhaps terraform an otherwise uninhabitable planet for this purpose - they might build a Dyson Sphere around a star. Close enough in, and the mass of the star and the sphere together should be enough to create a gravitational gradient suitable for moving about on the surface, and retaining an atmosphere. The nice thing about a Dyson Sphere is that it can capture all of the energy radiated by the star to run the Museum. A sphere like that would require some kind of station keeping to make sure the star remains at the center of the sphere (radiation pressure from the star isn't likely to be constantly symmetrical - one good flare, and the entire business would start to drift, with no guarantee that a balancing flare would happen to push things back), but for the intergalactic commonwealth that'd be a minor matter.
The main thing is, if they pick the right kind of star they'll have the energy supply for millions if not billions of years, and plenty of room for the museum.
The surface of the museum would be sculpted to simulate various natural environments. In fact, there might be dimples in the surface, similar to the dimples on a golf ball. Each dimple would contain an atmosphere suitable to the creatures whose museum entrances were located there. There wouldn't have to be a separate dimple for each species - that would be unrealistic - but it is not at all unreasonable to suppose that many species could comfortably share the same environment, even if they evolved on entirely different planets.
Supposing it were possible to arrive at the museum via spaceship, you'd be looking out onto the museum with various kinds of cameras that can give a view adjusted for the visual organs of whatever species happens to be looking. The surface of the sphere wouldn't be illuminated by the star, of course. Although it might be cool to have the thing set up in a binary system, any kind of binary companion would have to be pretty far away, so that its tides wouldn't disturb the museum. At such a distance the companion would merely look like a very bright star, producing less light than a full Moon on Earth.
No, if the surface of the museum is illuminated, it'd be by lamps of some kind. Perhaps there'd be arrays of lenses and mirrors conducting light from the star inside to shine out through the surface. Humongous balloons floating in the atmosphere in each of the dimples of the museum would have reflectors suspended on their underside. They'd be tethered above the light tubes, and the light from the star inside would then be reflected back down to the surface. Filters of various kinds would make sure that the light was suitable for the particular species in the vicinity, and the mirrors and lenses could be adjusted in case a diurnal rhythm of some kind was desired.
From space it would look a lot like those pictures of Earth's nightside, except that the light clusters would be evenly spaced out. Maybe it'd be more like looking at a gigantic disco ball, floating in space, with occasional rays of starlight glinting out at the cameras of the approaching spaceship when a reflector balloon gets pushed around by the winds.
But actually, I don't think that the Museum would be built all in one place. That'd be cool, in a fashion, but impractical. After all, it would require transporting visitors and artifacts to the Museum. There'd have to be hotels and the like at the Museum, too, since such a Museum could never be visited in its entirety in just a few days.
No, it is much more likely that the Museum would be distributed, with entrances (the same ones that won the architectural contests) located on most major planets. The exhibits would be available via sophisticated virtual environments that allow most sensory modes of interaction. Perhaps many visitors wouldn't even go there physically, but rather visit via some kind of intergalactic internet.
Imagine the exhibit for Earth. I imagine that the geological history of our planet is going to be remarked as fairly interesting, given that relatively few worlds of the millions or billions (perhaps only 1% or fewer) have a Moon like ours. For us this has had a number of important consequences, from stabilizing our planet's axis of rotation (and hence our seasons) to providing strong tides that might have hastened the evolution of life on land. I don't know if planets without those features could even evolve intelligent life, but if the can I expect their evolutionary history to be quite different from ours. While I expect the principles of evolution to operate in all places in about the same way, I don't expect the particulars to be the same at all, so the Museum's exhibit for Earth would include a list of species that have evolved here, as well as their evolutionary relationship to each other.
Our cultures currently aren't (as far as I know) members of the Intergalactic Commonwealth, so that detail would be noted alongside all parts of the exhibit concerning the history and cultures on our planet. Since for a long time - thousands of years - various levels of technological advancement existed simultaneously on the planet, the exhibits for each civilization would have to include information on its interactions with neighboring civilizations, and on its contributions to the human treasury of knowledge. I have no idea how the curators of the exhibit would divide up these civilizations. Their perspective on our history would be a deep time perspective, not the kind we use, fraught with tribal prejudices and mythologies. Assuming Earth was surveyed early enough in its history to catch the evolution of the human species, and thus note the rise of species capable of sapience, the exhibit has various options, ranging from following germ lines to following language groups. It's doubtful the exhibit would put a great deal of emphasis on tribal lines or national identities, since in the deep time perspective these things don't actually matter all that much. What would matter are milestones of human development, ranging from the taming of fire to formal education of our young to descriptions of the universe like the General Theory of Relativity or Quantum Mechanics. Cultural tools like public education might not exist among all species, but models of the physical universe should be pretty much identical, regardless who discovered them. Therefore I'd expect a lot more attention to be paid to when and how humans began to organize into communities with laws, and a lot less attention to when we discovered the wheel or orbited our first satellite.
Once the Earth does join the Commonwealth, perhaps the Earth Exhibit of the Museum would be moved to the Earth, and curated here by human scientists. But for now the exhibit could be just about anywhere. Since we kind of have to assume that some form of faster than light travel is possible (otherwise you can't really have an Intergalactic Commonwealth), the actual location of the exhibit wouldn't even have to be anywhere near the Earth, or even in our galaxy. However, the most likely eventuality would be that the species that originally discovered the Earth would have come from our galactic neighborhood, and they would be the ones who initially set up our exhibit.