Hadrian's Wall visit from Newcastle.

Three suggestions.
1. For Newcastle, Hampton Inn and Suites is directly across from the train station, clean, and reasonably priced.
2. To maximize your time at the wall, hire Peter Carney as your guide for the day. He will transport you to the key spots that match your interests and gives great information about them. I can’t recommend him highly enough.
http://www.hadrianswall-walk.com
3. For more time at the wall, don’t stay at Newcastle on arrival day, but take local train to Haltwhistle and stay at Ashcroft guest house. Start from there and give yourself more wall time.

I agree that Peter Carney is excellent, and he will pick you up at the Newcastle train station or your Newcastle hotel. Hadrian's Wall is fascinating, so staying closer to it might be a good idea.

Here is lots of information about Hadrian's Wall, including the timetable for the bus service between Newcastle and locations at or near the wall. It looks like you take a #10 bus to Hexham and then # AD122 beyond. I'd recommend Housesteads and Vindolanda. You should have adequate time the morning after you arrive, especially if you start early, and depending on when you have to be at the ferry. There may be more convenient bus service in the warmer months. You'll also want to leave your bags in Newcastle, either at your hotel or elsewhere.

We stated at a great Farm House B&B near Haltwhistle and did the Wall as well as the Roman museum and ruins. It was good. You may be able to do the Wall at a location closer to Newcastle.

I would strongly advise against taking the bus on your time schedule.