I know how you feel. It's the same with me. I hate being tired and sore and out of breath or whatever, but I love moving. Love it. I dance around the house. It's amusing.
Lol. xD Good luck, if you go. If not, I guess there's nothing wrong with finding out. Of course, at 5:30 in the morning, it also might be locked. I know mine would be.
I jogged for a few days, but then winter came around so I had to stop (so cold!). All I know is, you'd look pretty hardcore, eh? xD
I live right by the local high school, too. Lol. Now if only we could jog together! Dang distance.