Leaving Newcastle one heads North leaving the CTR while passing the market town of Morpeth, and on to Alnwick (with its large castle as seen in many a film/tv programme), then west to Rothbury & Cragside Hall (National Trust - and one of the first houses lit by hydro-electric.) Watch out for Eshott airfield a few miles north of Morpeth.
Wooler, gateway to the Cheviot Hills is next, looking out for the gliders from Milfield on weekends and the RAF Tornados if it's a weekday. The Cheviot (about 2500') is off to the west at this point. Next we turn East to cross the beautiful Northumbrian Coast heading for Holy Island only a mile or so offshore, a quick circle of Lindisfarne Castle & Priory. The priory is built near the site of monastery established by St Aidan in the seventh century. Depending on the state of the tide, Holy Island really will be an island, or if the tide is out, you will see cars and people making their way across the causeway. If you're lucky you'll see some brave souls making their way across the mud on the pilgrim's road. Lindisfarne Castle is owned by the National Trust and open to the public.
Heading south again we reach Bamburgh Castle, seat of King Oswald's, the man who asked Aidan to come to Holy Island in the first place. Bamburgh (not now Oswald's original castle) is also open to the public.
Seahouses Harbour and the Farne Islands are next. Watching out for the parachutists at Brunton and the RAF Sea Kings from Boulmer we continue passing Dunstanburgh Castle, Craster (of Kipper fame) and Beadnell harbour (the only one facing West on the East coast I'm told). Next its Alnmouth & Warkworth with its castle, past Amble marina (alas Freddy the Dolphin is no longer to be seen) before we happen across Industrial south east Northumberland with its vast open cast coal sites (I'm sure you could get a negative reading on your altimeter some are so deep!), Lynemouth & Blyth power stations (don't panic if you smell burning here!, but remember to call ATC since this is where the CTR begins) past the wind farm on Blyth pier and its time to return to Newcastle. However if time & air traffic permit you can continue South past St. Mary's Island with its lighthouse, to Whitley Bay & Tynemouth Priory then up the River Tyne to rejoin from the 'Five Bridges' and Newcastle City Centre, and thence back to the field.
Of course there are many variations on this and you can always break your trip for a coffee/snack at Eshott or Brunton airfields enroute.