There’s not that much north or east of Grosmont – head south or west – Cropton, Glaisdale, Rosedale, Danby, etc. The Rosedale ‘classic’ is a good one – start at Lastingham, head north on double track to Ana Cross, keep going cross road (chimney bank) follow old railway line all the way up to the head of Rosedale, right round and back down, dropping into the valley to pass Dale Head Farm/High House Farm/Thorgill, on to minor road to white horse pub just above rosedale abbey, pass front of this then follow Hollins Farm bridleway back to Lastingham. It’s thick end of 20 miles but you cover a lot of distance quickly on the old railway. It’s a nice intro to the moors!