Plymouth is a city in southwest England.
Hitchhiking here seems easier than elsewhere in England. There is no restriction to which roads you can and cannot hitch in and out of Plymouth as there are no 'M' roads.
North towards Tavistock and Okehampton
This is tricky. Your best bet would be to get the 83/86 and maybe the 84 (often changes!) until you get out of the city to a hitching spot of your choice (it really is that easy) ot all the way to Yelverton where the road splits to Tavistock or Princetown if you want to see some sheep, hills and prisoners.
East towards Exeter
There is 'Exeter road' which if you walk along enough will take you to a dual carriageway where it is easy to get a lift in the right spot, I will leave that to your discretion since I have no time to pull up maps,links and references.
West towards Cornwall
You need to find the 'Torpoint Ferry' there is a purple bus that will take you there and further if you want. Once in Torpoint you can walk a mile or so untill you reach a road with limitless hitching spots.