You can get on the Sowe Valley path here: https://goo.gl/maps/cnJNanB9BpR2
and then ride along to the hospital (UHCW). When you reach the hospital, head through the back (via the ambulance only exit) to Farber Road. If you carry on along the Sowe Valley path here it goes through some fairly rough areas!
Farber road then takes you to the bridleway to the back of Coombe Abbey. Turn right, to head south on the bridleway opposite Hillfields farm, that takes you into Coombe Abbey.
Then you can have a ride around the woods in Coombe Abbey and leave via the main entrance at the front. Rather than going along the road, you can go down the “twelve o clock ride” bridleway which brings you out by the old speedway track in Binley Woods (the suburb, not actual woods). But at the back (south) of Binley Woods is Brandon Woods, which is some actual woodland. Get to the junction of Craven Avenue and Ferndale Road and you can get into the woods. There’s nothing particularly technical in there, but it’s a pleasant place to ride around. You can just ride along the main tracks and nip off down little twisty bits as you spot them. It’s only small so you can just ride about aimlessly and then get back out relatively easily.
There’s also a few bits of bridleway a bit further out around Ansty/Shilton/Withybrook.