Wife's relations near Haltwhistle so never needed to check out accommodation. Using publuc transpirt, note that the main road between Carlisle and Newcastle has an hourly bus service number 685 ( already mentioned -less often Sundays and public holidays) and a train which also runs every 60 - 90 minutes, so in addition to the AD122 bus, there are occasional other services which link towns along the Carlisle -Newcastle route with the wall such as the 185 from Haltwhistle and the 680 from Hexham. You might find the bus info on www.northumberland.gov.uk/Highways/Public-transport/Bus.aspx worth checking out for most of the Wall area. Note the AD 122 bus stops for the winter, but usually starts up again around Easter.
As you're in that general area, note that to the north is the Kielder Forest, and to the south heading down towards County Durham lies Alston followed by Weardale and the area sometimes referred to as the North Pennines just in case they appeal. The scenery in the North Pennines is particularly impressive, but public transport very scanty as so few people live there.
Just to the south of this is the picturesque Eden Valley through which the famous Settle - Carlisle railway runs. Hope you're planning a long visit!