Pittsburgh offers great cycling trails, nearby hiking, backpacking, and water sports, not to mention TWO REI stores! The Great Alleghany Passage (GAP), starting at Point Park, offers a cyclist a trip to DC by connecting to the C&O. Nearby Raccoon Creek State Park, to the west, offers great day hikes and even an overnight. The Laurel Highlands, especially Ohiopyle, offers cycling on the GAP, white water rafting and kayaking, and hiking on the Laurel Highlands Hiking Trail. There are several small crags and bouldering areas within a reasonable drive.
We just moved to Pittsburgh last year and have been so pleasantly suprised with all the outdoor activities! Ohiopyle is amazing - it was the first camping trip that we took after we moved. I can't wait to check out the rest of the items on your list.