Lots of walks in and around the Park although no direct access from the CC site now (gate blocked) but only a short distance out to the road & back into the Parks side entrance. No cycling allowed in Cirencester Park itself, walking only.
We used our bikes & there are plenty of quiet roads & cycle ways to explore, including an easy run into the town, although its a bit of a drag back up to the site - nice though.
I'm sure you'll enjoy it.