Wyoming is the second most underrated state, Utah the 3rd but the MOST underrated state is without a doubt Montana. North West Montana is perhaps the most gorgeous part of the US. The last best place, the last best people.
May can actually be a great time to explore the lower trails. As you get higher the temperature is fair but you're walking through partially snow covered hills etc. It's beautiful and there are far less people at Glacier to contend with. My favorite trips there have been in May. You're right though, if you're interested in some serious back country hiking May will not work, but for camping and day hiking he should be all set.
He also specifically mentioned loving to travel by car. There's no better drive in the world that I've ever seen than Going-to-the-Sun road (I think that's the name anyway--the one that goes through Logan Pass). That will blow your mind, but no way you can do it in May.
Thanks for the tips, y'all. I do like traveling by car, but we'll be driving to a point and then hiking w/tent etc if we do this trip (it's not dependent on me so I haven't done any research yet). If May isn't as good for back country hiking because all the trails aren't open, we may adjust and camp in different places every night by car. Either way, really.
Let me know prior to going, I may be able to help steer you in a right direction. It's a wonderful place.