Excellent! Hamilton is a great smallish (for Montana) town. It is a STUNNING valley to live in. It's developed a nice younger culture also. The entire Bitterroot is pretty sweet to live in. While most folks will be commuting to Missoula, you won't have to! It's gotten pretty chopped up, lots of development but it probably won't seem like it to you coming from CO.
Lost Trail is about an hour to the south. It's nothing steep, but they get a lot of good powder. Mom-and-pop area with little grooming. Used to be tiny, but it expanded and is a decent size. Plenty of backcountry opportunities but they have a long approach.
There is a kayaking creeking scene in the Bitterroots, but it's mostly hike-in creeking. River running is a bit bleak, the Bitterroot river is mostly for fishing and hot summer floating/canoeing/tubing. You'll have to head up and over to the Lochsa (2.5 hrs) or hit the rivers around Missoula. If you head south, you can run the day section of the Salmon which is really sweet. I've not run it, but driven by in June (coming out of MF), and it looks like it'd be a good second choice. That's probably 2-3 hours. Head even further south to the Stanley area and there's more Salmon River boating, but I know nothing about that area.
It is a bit hemmed in N/S, you pretty much have to go 1 hour north or south to get out of the valley. In the summer the road is open over to Rock Creek, a supposed renouned fishing river/creek.
Lots of rock climbing I hear, and mountain biking up at Lost Trail and also to the east. Probably some SW of Darby also.
Living in Montana, boating in Idaho