How do I get to Hadrians Wall from Newcastle on Tyne without a car
Take the train to Haltwhistle. There you can transfer to the AD 122 bus route right at the train station. This bus will stop at the key wall sites.
Another option is to take the train to Hexham and hire guide Peter Carney. He will provide transportation and give you a wealth of background info that will make this very interesting area come alive.
I’ve used both methods. I learned so much from the tour with Peter that when I explored the wall on additional days by bus/walking, that I felt like I knew much more about what I was looking at.
We visited Haltwhistle (stayed at a great B&B on a farm) and drove to the Wall area and museum. It was nice.
Or, as the link Carol provided shows, you can take the train or a bus to Hexham and get the AD 122 bus there, without hiring a guide. (Nothing against the guide, just covering all your bases.) Hexham has a very good church with a Saxon crypt and some Roman items. Along the wall we loved Vindolanda and Housesteads, we didn't get farther west but I'm sure there are more great places.