This large forest in Suffolk has miles of good footpaths and a 10 mile red graded single-track mountain bike trail. The waymarked route is called the Viking Trail and is a narrow flowing singletrack running through the trees, with twists, berms and some short climbs. It's a fun ride and not too challenging though there are some technically tricky bits. The ride starts at the car park off Tunstall Road towards the northern end of the forest.
This mountain bike route is designed for cyclists but walkers can easily pick up the forest footpaths from the same start location. You can walk down to Tunstall Common and then continue south to the little village of Chillesford for refreshments. From here you can pick up the Suffolk Coast Path to take you back into the forest and then head west to return to the car park.
If you'd like to continue your exercise in the area then you could head to the nearby Rendlesham Forest where you'll find family cycle routes on flat well defined paths and quiet country lanes. For walkers there are also two way-marked trails of differing lengths.
Also nearby is the splendid Orford Ness Nature Reserve. The national trust owned reserve is located on a remote shingle spit by the River Ore and can be accessed by catching the National Trust ferry from Orford Quay.