Answer:
Well I'm no ecologist, but a quick glance at google maps shows that Yellowstone and Grand Teton National Parks and surrounding National Forests form quite a large forest area, but the cluster of National Forests to the west in Idaho make up an even larger continuous grouping: Sawtooth, Boise, Challis, Salmon, Payette, Bitterroot, Nezperce, Clearwater, Lolo, Beaverhead, and Kootenai forests make a pretty much unbroken chain of wilderness across much of Idaho.
This obviously isn't one unbroken stand of trees, so you'd have to define "forest", but as far as set-aside National Forests, that's my vote. Then there are Wrangell-St. Elias and Denali in Alaska, but if it comes to that then Alaska in general is one huge "forest" that's as big as half the continental U.S. itself.
If you're talking about getting as far from human civilization as possible (in a forested terrain), I've heard Yellowstone is about as good as you're going to get, but even there you're never more than about 20 miles from a dirt road. For that you have to go to Canada/Alaska.