Woodbury Common is South West of Honiton. Take the Sidbury road to the south and turn right at Sidford. If you're walking: just get the number 9 to Exeter and ask for Joney's Cross Car Park. If you keep your eyes out for Newton Poppleford (big village to the east of the common) you know that you're about 3 stops away.
You're not to far from me (Axminster). There's an old hill fort called Blackberry Camp. It's not so much for hiking but it's a nice woodland with stunning bluebells. There's no walls left because they were wood but the mounds are still there.
Sidmouth has a nice walk from Sidford along the Byes. Haven't done it myself for years though.
Lyme Regis and Charmouth aren't to far from Honiton Either with nice coastal walks and you can also walk right up onto Golden Cap.
There is a short coastal walk between Seaton and beer that's good and Beer is a very picturesque fishing village. You could then go onto Branscombe.
There are plenty of good local walks around. I follow a Facebook page called Flipflops and Wellies who IIRC have a website too. You can also get maps of local walks too.