Unfortunately, not much is near BTMRR. It's at the top of a relatively steep hill and nothing else is up there. Splash Mountain is at the foot of the hill, then further on are the barges for Tom Sayer's Island (which I imagine would be both too long an excursion and more fun to do as a family) and further still is the Country Bears Jamboree.
However, there is plenty to SEE, if you don't expect the wait to be too long. There's a nice overlook where you can watch BTMRR go around. You can also look down over the rest of the park, watch the barges and Liberty Queen ferry boat and/or grab a little snack at one of the carts in the area.
The only nearby gift shop is for Splsh, and it's down a bit of a hill and not very large, so I probably wouldn't go there unless you need some a/c.