I live in Cornwall and work in Hampshire and the latter has many more opportunities for riding off road. Where Cornwall has tiny lane joining single houses, or three lanes without any houses that seem to go to and from nowhere, Hampshire has a big field with a track through it or a bridleway alongside it.
There are bits of bridleway and byway, but you work hard with an OS map to join them into a route, or pinch the odd bit of footpath early in the morning or on a night ride (but many of these mean hopping over a kissing gate or stile at every field boundary).
You can ride the lanes on an mtb and will meet little traffic and get some great views. You’ll also get a good workout as my normal rides here are 50% hillier here than Hants. Many of the lanes will be muddy and potholed, but they’re not swooping singletrack and personally I find an mtb the wrong tool for tarmac riding, even when some of the hills suit an mtb’s gear ratios!
You’ll probably pass Haldon Forest, near Exeter, on your way down and, as has been mentioned, Cardinham and Lanhydrock are about an hour away if you want fun, fairly easy, trail centres with parking and a cafe.
If you want some downhill and will pedal back up then Gawton and Tamar Trails centres are also about an hour away. Both need online payment as a guest. I’ve ridden Gawtons HSD on both a hardtail and FS and had more fun on the latter. I’ve also survived down Proper Job, but need more training and longer suspension to really do any of the others any justice.
You’re 45 mins from Okehampton which gives you access to the northern section of Dartmoor. Be aware how exposed you are on the moor at this time of year and dress accordingly.
Hope you do manage to get out and enjoy the area whatever you decide. The coastal path is spectacular, so if you can bear to bring boots instead of bikes, you might be making the best use of the area.
I’ll now go and was my mouth out with soap for suggesting that on STW
