There always seems to be something cool happening, and if not, there's definitely always some solid natural scenery.
Play ping-pong, check out a book, and play some putt-putt. Not simultaneously. That would be difficult.
Why pick green space or city when you can have both? Main Street Garden Park is smack in the heart of Downtown.
Why limit yourself to ONE Downtown garden? Belo Garden features plenty of native trees, gardens, and a fountain plaza.
Or walk. Or ditch the whole free thing and head to Katy Trail Ice House for drinks. Or keep up the whole free thing and stick a friend with the bill.