Yes and yes. If that's what you want to do, look at ski resorts and find out what their summer activities are. They all have very reasonable prices (if that's important to you). Also look at New Mexico. Santa Fe is really, really nice this time of year. (And although I've never been there, so I can't recommend it, Montana.) You've got me longing for the mountains. As soon as I finish this start up at work, I might book a trip. Edit: This looks fun.
Do a cruise to the Bahamas, but get there a night early and hang on in Miami...Very romantic... Edit: Mountains? Well, I would then suggest Durango Colorado or better yet, Banff...Been to both and can't go wrong...Banff is better...
Couer d'alene, ID is nice resort w. good golf. Jackson Hole, WY for mountains. Also, might want to check Charleston and Hilton Head SC.