We've never been to Provo, but there seems to be a lot to do outdoors, even in the off season. It's right in the middle of a huge mountain range (the Wasatch). There seem to be many hiking trails in the area. This site can help you find one.
There are even trailheads located right at the campground! You can take a short walk (3.4 miles round trip) to Stewart Falls, or a longer 14.7 mile walk (round trip) to the summit of Mt. Timpanogos. Both hikes look pretty stunning.