Though it's MUCH smaller than nearby Elmwood Cemetery (my preferred place to go for walks, to walk my dog, or to read the paper on a sunny day--no, I'm not goth), Settler's Cemetery is a great place to hang out, and it's literally a street over from the center of downtown.
From a historical perspective, Settler's is worth checking out if only because it houses some of the oldest graves in town--super old (hence the name). These are definitely worth checking out.
On top of that, the cemetery is beautiful--lots of grass, and lots of benches to relax on. It's a good place to take your dog, too: there are normally tons of other dogs and walkers hanging out here.
A little open air and space is a nice change in downtown, trust me. Make use of it.