I have to say Estes Park CO.
1: Gateway to the Rockies, there are multiple entrances to the park from Estes. That really get you into the mountains with out having to hike. Trail ridge road will take you about as high as you can get (I think it's the highest elevation road in the US). You will see big horn sheep, elk, moose and bear more than likely depending on season.
2: Activities: There are several places in estes to horseback ride. You can choose from meadow rides or up the rocks into the mountains (id do meadow with young kids). You mentioned white water rafting, It is a short drive into fort Collins to raft the poudre but it depends on when you go, later in the year the less appealing it is to have kids on the river the shallower it gets (more likely to tip). There is also a fun park that has bumper cars, go carts, water rides, some kind of kids obstacle course that looks awesome, a big tram that takes you way up, multiple trout ponds that you can catch your own dinner (think closed real not fly rods). Kids love catching those big trout. The Stanley hotel is also located in Estes and even if you don't stay there, you can spend half a day just walking around it. It is where the shining was written and parts of dumb and dumber were shot as well as one of the most historic hotels in the world. There is also a couple of decent breweries to check out and multiple good cheaper restraunts.
3: shopping, main street has about 60 stores, you can easily spend half a day just walking up and down looking at stuff.
4: hiking, with little kids you wont want to do Longs peak by any means but you can do alluvial fan and alluvial falls in horseshoe park (inside rmnp) that will make your kids think you just hiked a while when in reality it took about 10 minutes, you could also go to bear lake ect which is pretty awesome short little hike.
Ive made that town my second home every summer since high school and while there is less touristy and more isolated places by far in the rockies, no town ive been to has the variety that Estes provides.