Further to my previous post, here's a few more that you may wish to try.
If you want to walk on Dartmoor, get the bus from the City Centre to Yelverton, then another bus from there to Princetown. Buses to Yelverton are quite frequent, but the ones to Princetown are less so, so you will need to check the timetable. The Dartmoor National Park Authority have an excellent Visitor Centre in Princetown with very helpful staff who will be able to point you in the right direction for various walks, but one good one is to walk along the former railway line that used to run from Plymouth to Princetown. (If only it was still running
). This walk affords fine views over southern Dartmoor and takes you past the disused granite quarries at Foggintor which are worth a look around.
There is also a good walk to be had at Bere Alston, which is on the Tamar Valley rail line which runs from Plymouth to Gunnislake. (fortunately this is one of the few branch lines that is still open
). From Bere Alston there is a good circular walk which follows the River Tamar for much of it's way, or alternatively you could walk to Bere Ferrers station and get the train back to Plymouth from there.
You could also get off this train at Calstock, which has a beautiful Victorian railway viaduct crossing the Tamar. From there you can walk through woodland to the National Trust property at Cotehele House, then it's a short walk downhill to Cotehele Quay. One of the old Tamar sailing barges is moored here that used to transport the locally grown fruit & veg to the docks at Plymouth.
One final walk - this one starts in Plymouth. Get the bus to Tamerton Foliot, which is a village on the outskirts of the city. Walk from there through quiet country lanes, fields and woods to Lopwell Dam, which is a picturesque spot on the River Tavy. From there you can walk back to Tamerton Foliot by following the river bank for most of the way.
I hope this gives you some more ideas. You will need to get the relevant OS maps for the area to pick out the footpaths.
Enjoy your walking!