Actually, I seem to recall that Mars is within the range as well, though the safety margins would be (much?) smaller. You also already have a nice big counterweight already almost in position on Mars, in the form of its outer moon, which is very nearly in "Mars-stationary" orbit (though the existence of it's inner moon would present some challenges)
On either world though, while it would be within the limits of current material science, I'm less sure it would be within the range of current engineering ability. Certainly it would not be anywhere remotely near the first project you'd undertake - you'd want a thriving self-sustaining industrial base on site first.
Consider, the orbital dynamics demand that a Lunar elevator extend at least a little beyond the Earth-moon L1 or L2 points, meaning you'd need to build a 60,000 km long tether - long enough to wrap one and a half times around the Earth. It would be by far the largest engineering project ever undertaken by humanity. Building self-contained cities on both planets would likely be a cakewalk in comparison.
Where space elevators are concerned, skyhooks are a much more realistic option - far smaller, far simpler, far lower demands on materialproperties, and with no moving parts they act as roughly 100% efficient momentum "batteries" to transfer momentum between launching and landing vehicles. On the moon you could even theoretically build them to grab stuff right off the surface and hurl it on a transfer orbit to either Mars or Venus. (Ironically, assuming the lower end is near the surface and syncs with surface speed, the smaller the skyhook, the more powerful it will be)