"Trump would most likely just demand they add more floors to an earth-based tower until it reached space :-)"
Such a thing could possibly be done on Ceres and anything smaller. Some falling rocks even have littly, baby rocks already in orbit around
them that could be used for construction materials or asteroidal-stationary mid-points.
Maybe Pluto, too, though a Pluto-Charon Bridge might be more fun and easier. For a Plutonian Orbital Tower one would probably need to spin-up
the planet so the "centrifugal force" could be high enough to keep it upright. Looking at it another way, we'd need to create a viable stationary orbit
for the Plutono-stationary centre-of-gravity of the tower to live in. Spinning-up a planet is simple engineering and highly expensive economics. It
would do things to the P-C barycentre. Maybe.
Eros could have a launch tower poking out. Maybe two, for symmetry.
An orbital Tower on Venus would have to be large enough to reach half-way to Mercury. She doesn't rotate very very rapidly so cythero-stationary orbits
are extremely wide. Spinning up Venus would be a tiny bit beyond Man's present economic base. Though, if done, it would help with Greening the place.
Note: I said "easier" about the Bridge, not "easy". :)
I wonder whether, when Mr. T. wins next year, we could interest him in building things like these? As Vanity projects, they would quite literally be out of
this world. Why have a face carved into one tiny, obscure hilltop when one could use entire *worlds*?