It's great to hear some people mentioning places I also think are great!
Zion-I lived in vegas and took my wife on our first camping/hiking trip here. Awesome scenery and really easy access to hikes.
Red Rock Canyon-Weekdays in spring or fall are the best, way less tourists. Really good climbing in the Calico basin, really good mountain biking on the other side outside Blue Diamond. Also, the 12+ mile scenic loop that is bumper to bumper on weekends is basically a sportbike track on weekdays. There are only a couple of spots where rangers park, if you're not being too outrageous you're free to rip it. So many low speed corners you never get fast enough to do much real damage.
Alaska-I've worked up there quite a bit and have some great memories. Hiking/climbing flatop mt outside anchorage, bombing around a co-worker's dirt road neighborhood in quads, seeing moose in town, hammered in downtown anchorage in the middle of winter and giving the corporate logo coat I just got to a homeless dude, haha! Denali is awesome and vast. My favorite place is Juneau. I did an 8 mile trail run that was pretty magical (Perseverance trail if you're ever there), fresh crab down at the docks, short drive to the mendenhall glacier. The misty hills right next to town are amazing.
Western Cascades, WA-I live here currently and bitch all winter. But these mountains are amazing as well, especially in the summer. Everything is so green, and there are so MANY trails, campsites, little known lakes it's easy to get away from people even really close to Seattle. The mountain biking especially is incredible here.