Don't leave the airport. Too far to away to go anywhere within your window without being stressed out and constant watching checking.

The upper mezzanines of any concourse are quiet and good places to relax and read.

Or you can exit security via the train to the main terminal and wander around. You can see Pikes Peak from the south end of the main terminal building on a clear day. They have various art exhibits on the hallway to concourse A (on the north side of the terminal.) Some are interesting - last year they had old skiing gear from the 50s and 60s.

If you HAD to leave I'd suggest a cab to Lulu's Bar and Grill in Watkins. Have a burger, play some pool, chill with some bikers, and go back to DIA.

By the way where is your second flight to? I'd suggest just getting an earlier flight if one avail.