Based on your suggestions, I’d go for a road ride north towards holy island would be good. Assuming you start in Morpeth it can be done a variety of ways using mainly back roads at about 70 miles (one way). Check tide times though for crossing and maybe have some train times from Berwick or Alnmouth if you want to do a one way trip.
Basic route is towards netherwhitton, rothbury, thropton, powburn, (cross main road) eglingham, christon bank, newton by the sea, bamburgh, belford, (then a short stretch on the A1 is unavoidable with a road bike unless detour west of kyloe), beal, lindisfarne. A map would be necessary if you don’t know the area.
Alternatively, from powburn you can keep going north (rather than turn east) through chillingham or wooler (or both) and then ford, lowick, beal and lindisfarne. Or go inland for the route up, skirting the hills and come back skirting along the coast to make a nice loop. There are pubs in nearly all of the places listed (and some others you will go through).
Should all be pretty obvious with a map and the back roads are dead quiet, with very few big hills. From holy Island, if you want to get a train back, head north to berwick, and either side of the A1 you can find ways that will keep you out of the traffic – though with road tyres, to the west is probably the best bet.
[edit] and I’m working ,or else I’d consider it.