Once you get to Moscow, you'll joke about the fact you even had to ask if an outdoorsman would enjoy the immediate area.
As a wilderness-lover who attended the U of I, I could write a book and still barely touch on all the things the Palouse and Clearwater have to offer, not to mention Washington, Montana, and Canada within just a bit more of a day trip. Lots of ski areas and lakes around. In the summer, the ski areas become a sparsely populated haven for mountain bikers, who can use the lift if they just want to be crazy without the climb.
As you go South, there are plenty of areas to access the ranges of the Frank Church Wilderness (look it up if you don't know about it already... a great place to put a LONG distance between yourself and civilization). Any backpacker with confident endurance and self-sufficience will quickly be drawn to buy maps of the Frank Church areas east of Grangeville and Riggins. If you drive the White Bird grade getting to Moscow, stop at the Chief Joseph's Last Stand memorial and check out the view... you'll see why those maps are coveted.
There are trails, lakes, streams, and springs all over in every direction from Moscow, many within no more than two or three hours, usually less. Much of this is inhabited with edible berries and mushrooms to complement the light packing of granola and oil, respectively.
Aside from a few areas right around ID-95 on the South side of town, Moscow is extremely bike friendly. Often, I could get around Moscow faster on a bike than in a car. The hills will give you exercise, but once you adapt to them, biking on any grade is a cake walk. There's even a great bike trail from Moscow to Pullman, so locals learn to enjoy both towns and a moderate - but apparent - workout in between.