Cosmo has answered quite accurately: STL has 5 concrete accessible parking spots which connect to extensive concrete walkways that provide access to telescopes, the observatory dome, and accessible restrooms. The Nature Trail of native plants, however, is not paved, although the surface is pretty firm and probably will accommodate your electric scooter. Just to be clear: STL is an all volunteer nonprofit organization that is completely separate and outside of Joshua Tree National Park.
Yes there are concrete paths to various stations that can be used to set up viewing. Also the parking lot is packed gravel. Be a good idea to have a small light to find your way. Preferably something red so that it doesn't mess with others eyes when adjusted to dark
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