We were there a few years ago. If I'm remembering correctly, the museum is in what used to be a movie theater. While the story of the downed UFO and the newspaper reports are interesting (
something certainly happened back then) the whole museum and the exhibits are very amateurishly done. Lots of pegboard displays with photocopies and hand lettered signs. Not unlike something that a 4th grader might do for a science fair.
In general, we were really disappointed with Roswell all together. For being the great UFO city, there were just a couple of knick-knack stores down from the museum that looked like they were former jewelry stores now selling green rubber trinkets.
We are not big UFO believers, but we do enjoy Sci-Fi and watched the Roswell TV show (with Catherine Heigl) from several years back. So since we were travelling through New Mexico, we thought we'd check it out. It doesn't seem like they take any of it seriously or with any sort of scientific slant, but just play to the campiness of it. The museum did have some more serious information, but again it was very poorly presented.
But am I glad we stopped and checked out the museum? Yes. How can you go through Roswell, NM and not visit the Alien Museum?
As for the parking - it is just like any other old downtown area. Street parking in front. Others have said there are parking lots nearby...could be true.
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And here's a photo of the cheesy knick-knack/TeeShirt store down the block: