As per my post below, I want to visit Hadrian's Wall. Not for a big long walk - next time when I've got more time - but for a little peak and poke around. Where is a good place in the North East to access the wall/forts etc.?

Easiest is Wallsend - 15 minutes on Metro from Newcastle, turn right and you are at the - em - Wall's end
But presumably you want a bit more countryside. Then the best options are bus or train to Corbridge, Hexham or Haltwhistle then take the see connecting bus service onto the Wall -

This places is okay for a little poke about :- Museum of Antiquities - Newcastle
South Shields also has the Arbeia site with rebuilt wall/gateway - this too is on the local Metro route, about 25 minutes from Newcastle.

There are various sites around the main area.
Vindolanda is a fort, with restored bits, musuem etc. Touristy but informative as well. Houseteads also similar. Both are close to Once Brewed. Once Brewed visitor centre has lots of information as well. Segdunum at Wallsend is much closer to the city centre, but Housesteads and Vindolanda are in lovely scenic countryside and so much nicer.