Since you want to be close to Centennial, start with
H E R E - CO State Parks
, scroll down and input Cherry Creek and Chatfield SP. These are both close to Centennial without having to drive far. Both are excellent state parks, with full hookups and/or electric only. I'm pretty sure there is a 2 week limit, but you could stay at one and then move over to the other, if you're going to be here more than 2 weeks. There is a 180 day/6 month booking window so if you have dates in mind watch the booking window very closely as they both book really fast during the height of the season. There's a lot more info om the CPW website.