We went to Cutteslowe and Sunnymeade park on the outskirts of Oxford. Plenty of parking near the park (free). Run by local government. Has nice playground and a mini golf which is very nice for children and adults. You rent the clubs and ball at local kiosk for a few pounds. Also sell refreshments, ice cream, drinks etc. Plenty of space for picknicks, cycling, running. On some days they have a miniature train running. We enjoyed it a lot.