It isn't a hot bed of music, but there is a blues cafe bar on Montpellier parade (v close to Betty's) that has been going for years. I haven't been for many years, but given it is still there you can assume it is still decent.
http://www.bluesbar.co.ukLike the traveller's rest if you want decent pub food. It is on crimple lane about 2 miles out of town. I would link but on mobile and may lose the post. Edit.
http://www.thetravellersrestharrogate.co.ukThere is a farmers shop that does good food on the show ground. The attached farm shop has good local produce. All proceeds go to suicidal farmers. Will edit when I remember the name. Edit http://www.fodder.co.uk/shop. Fodders is only open til 5, but does afternoon tea 3-5. If it stops you queuing outside bettys in the rain for a four quid cup of tea, it can only be a good thing.