I had lunch at The Honor Oak yesterday. It has a huge outside area with some cool timber booths. Had their chicken burger which was delicious.
The Railway Tavern also has a huge garden. There is a raised bit of this, more of a large patio where no smoking is allowed. Smoking allowed elsewhere.
The Hill Bar and Lounge also has a small garden at the back. But as no one seems to know about it there is usually room when others have none. They even call it the Secret Garden.
Both the Dartmouth Arms and the Signal have small gardens, though the Signals is covered. I'm sure you've seen the one at the Sylvan Post.