You can’t go wrong with Surrey Hills for riding! Mickleham, Ranmore, Norbury and East Horsley all have some great trails, and as everyone has said you are not far from Leith, Holmbury and Peaslake by either ride or car.
Nirvana is a great first stop for people new to the area. Their rides take in a lot of the Leith hill and Ranmore area and they know all of the trails. Jumpy freeride practice loop on Saturday and a slightly more XC loop on Sundays. Great to get to know people and the trails.
Then for Peaslake you have Pedal and Spoke who know those hills as well as anyone. Both great bikeshops with great people. And I’m not employed by either!