Fabulous beaches in Northumberland - miles and miles of sand at Bamburgh, Dunstanburgh, Alnmouth and Druridge.
Castles - Warkworth, Alnwick, Bamburgh, Dunstanburgh
Lots of roman stuff along and around Hadrian's Wall - Housesteads and Vinolandia
Inland - Fielder Forest for mountain biking.
Urban fix - Newcastle - Centre for Life, Hancock Museum, Sage Centre, and you are not far from Edinburgh
Boat trip to Farne Islands
Lindisfarne - drive over causeway (check tide times!), great chips at The Ship! more beaches and castles!
Morpeth is nice for a potter.
Alnmouth is beautiful
Hexham is also nice.