So many choices… Ok, my recommended spots along the coast going south to north would be:
Amble (good for fish and chips) Warkworth – many pubs, Alnmouth. Craster Dunstanburgh – Embleton and Newton by the sea – great pub in the last one right by the lovely beach. Then you’ve got Beadnell and Seahouses – both a bit daytrippy but ok. Next up, Bamburgh and Budle – both terrific beaches. North of there is Lindisfarne which is worth a pedal over but don’t get trapped by the tide…
There’s really loads of places, I’m not sure about bivvy spots particularly and a lot of the coastline is NT / AONB so unsure about camping restrictions bit you can check.
If you want to head inland to the hills then you could aim for Wooler and Rothbury as bases. Happy to throw some more suggestions out if you need.