Carlisle is a nice city, and worth a visit in its own right (the tiny cathedral is lovely, and has excellent music).

My favourite sites on the wall are Vindolanda and Corbridge, both accessible by train (although the former has a fairly limited service). Vindolanda is within (30-40 minutes') walking distance of Bardon Mill station, and Corstopitum is in central Corbridge (a lovely little village) which has its own station. From Vindolanda, you can also walk to Housesteads and back to Haydon Bridge.

Both are on the Tyne Valley railway line, that links Carlisle and Newcastle, so you can start in either. If you buy a walk-up ticket from one to the other, you can break it as many times as you like. Train timetable is here.

In addition, if you want to see more sites along the route of the wall, there is a dedicated bus service that runs in the summer.