Amazing views from Trinity Mountain
The Boise National Forest has over 2 millions acres of pristine northwest wilderness full of pine forest, mountains, streams, and lots of wildlife like elks, bears, deer, and coyotes. As I said, the park is huge, so you should be a little bit of investigation before you go and decide what you want to see and do...after all, Boise National Forest has over 200 lakes, 500 hiking trails, and dozens of campsites.
Personally, I'd suggest driving up to the Trinity Mountain Recreation Area, the highest point in the national forest. Once you get there, you can make a short hike to the Trinity Mountain lookout (over 9,000 feet above sea level) and lake in one of the most spectacular views in Idaho. If you go after the snow melts, the alpine lakes will be full and the whole place will be covered in wildflowers.
Also, you might consider a kayaking trip on the Payette River during its course through the park. There are lots of little hidden beaches and campsites along the river and there are some companies in the area that'll rent you kayaks or even take you rafting if that's what you want to do. Seriously, Boise National Forest is beautiful. If you don't want to do something so active, you should try to rent a cabin. The cabins are spaced far apart so you won't be crammed between RVs and other campers. It'll make you feel like a true mountain man!