The Neon Museum (or the "Boneyard," as it's sometimes called), is pretty cool. Take the guided tour, preferably after dark (really all the tours are guided - you can't just wander around by yourself). While most of the signs have not been restored (it is *ridiculously* expensive to restore one so they are doing them as they raise the money), they have lights around the paths so you can see them. The ones that have been restored (like the Sahara and Stardust signs) are really neat to see up close. They also have a couple of signs out along the road nearby (one of their goals in restoration is to place some of these old signs around Vegas - some are already up in various locations). On this tour, you'll learn a good deal about the history of Vegas and the evolution of the signage.
The tour takes about 45-60 minutes. There isn't much to see before the tour: you can admire the lobby building architecture, browse the souvenirs, or explore some info on Vegas via electronic thermal screens (you move the cursor via the heat of your body sensed by the camera - you have to see to understand). So really, you don't need to get there very early.
They sell bottled water for $1, which was very nice in July. Parking was free. I'd recommend getting tickets online in advance, as these tours seem pretty popular.