Another thing I ALWAYS bring to the park is two beach towels.
I just roll them up real tight and but them in the bottom of the bag until we need them . . . and we always do!
They are perfect as a pillow for a nap, a sun blocker to hang on the stroller, a drape for the stroller if it looks like it's going to rain and as a TOWEL, when it does rain and you want to wipe everything off . . .
Right now we are prone to the 2pm-4pm thunder showers . . . so bring your ponchos too!