Regarding Hadrian's Wall - the Segedunum Roman Fort, Baths and Museum (also see the wikipedia entry), in Wallsend just east of Newcastle, is worth a visit should one be in the area. It was a fort at the easternmost end of the wall, and having been excavated it is now a museum - as well as various exhibits it includes an observation tower to gain a bird's eye view over the site (which you can also walk around), and also a fantastic reconstructed Roman bathhouse (which apparently can 'work' as a proper bathhouse, alas this isn't something the public can experience).

It can be easily reached from central Newcastle on the Tyne & Wear Metro - journey takes 10 minutes, trains run every twelve minutes, get off at Wallsend station and look out for the station signs in Latin! The Segedunum is just around the corner from the station.