I always enjoyed taking Eb to the local parks. Was well worth the year pass for state parks. Like AKBull says, be ready to pack ... stuff ... out. Aside from designated dumping stations in the campgrounds lots of parks aren't going to have regularly spaces trash cans. I got in the habit of double-bagging and making sure I had a segregated part of my bag/pack I wouldn't mind carrying it in.
Our parks also have leash laws (as well they should) that specify leash length. I hate those super-long retractable leashes anyway so it was never a problem but I'm used to seeing a 6-ft limit. I used a traffic lead on Eb so I could always get her under control fast if we ran into other dogs on the narrower trails.
All in all, hiking with your dog is an excellent form of exercise and lots of fun (especially for the dogs, getting new scents, meeting new people, etc.) and I definitely recommend it. Just be polite to other hikers, ALWAYS clean up after your dog, and either bring water or hit a park with its own water (lots of rivers near us, so we don't usually have to bring water, but bringing a collapsible doggie bowl would be a good idea). As long as I'm throwing out recommendations, I'd also say to bring a small first-aid kit. Both for yourself and the dog. Tweezers (splinters/thorns), all-purpose ointment, a bandage or two, etc. Doesn't have to be fancy.
~Marrow