Robin Hoods Bay has a folk Club on Friday Night. Whitby has clubs and sessions on Wednesday and Sunday. So no problems on the music front.

You can easily spend a couple of days in Whitby - Pannet Park Museum is an absolute must.

Scarborough is good as a wet weather venue even out of season and for a fine day a trip on the North Yorks moors railway can be fitted in with a ramble.
I love to get the train from Grosmont to Goathland and then walk back (mainly downhill) to Grosmont.

Pickering and nearby Helmsley are also pleasant market towns with Ampleforth also worth a visit.

Northwards (up the coast) brings you to Teesside with the Captain Cook Trail.
Also check out Guisborough, Northallerton and Thirsk.

The area is alive with wonderfully warm welcoming communities I am sure you will really enjoy yourselves but you may find you will need to drive to take in some of the attractions I have mentioned.