Destination Expert
for Barnstaple, Robin Hood's Bay, Whitby
I would certainly say there is more than enough to keep you in Bath for a entire day.
You could then head from Bath to Wells and have half a day in this lovely little city. The Cathedral is glorious and it is a great place just to wander the cobbled streets and enjoy:
http://www.wellssomerset.com/
You could then continue on to Glastonbury, the town is nice enough with lots of quirky little shops and cafes, it is well worth walking up to see the Tor, too, as the views are wonderful:
www.glastonbury.co.uk/pages/site.php?pgid=1
Chedder Gorge is also very impressive whilst in Somerset, so you may want to consider some time there.