Running will destroy your body. It's like taking a jackhammer to your skeleton! I so love the fact that after I ride, I am never sore. Tired leg muscles yes, it can be a challenge to stand up from sitting sometimes, but no pain. Not so with running.
(However I do play in a pick-up game of Ultimate about once a week, I love ultimate, but it always leaves me sore)
For an alternative second exercise to go with cycling, I would suggest push-ups. Cycling for the legs, push-ups for the upper body, trunk, back. (Those'll leave you sore too though!)