If I always ride at leisure pace and avoid uphills, how many and what health benefits do I still get from cycling?
You're still burning calories because you're moving. While you may not be burning them up as fast as someone speed-riding, you're still benefiting by working your muscles and cardiovascular system. You will still gain some leg muscle as you're using them, but as others have said, you won't be riding the TDF anytime soon.
IMO, you'll probably get more out of it in terms of mental health benefits; relaxation, time to think, etc. I do my best thinking when I'm just out on my bike pedaling away with absolutely no goal in mind. I find myself in this "dream world" and just..."ponder." I come home from a ride feeling refreshed and renewed, not with quivery legs like I just took a body-check into the boards by Scott Stevens.
