several parks I have been to, including the one by my house have an old school workout station with pull up bars benches, some that are on an incline with a guide of how to exercises where you can do pretty much everything you speak of and then some, and its away from where the kids play."Pushups and pullups can work wonders."
Parallel bar dips are, I think, the king of upper body exercises. Many parks have parallel bars, or you can often use the equipment in playgrounds to do them, as well as chinups. You just have to chase the little kids and their mothers away.