If your still looking areas to avoid
Efford, ham, swilly, eggbuckland, keyham, if you can afford it I'd stay away from devonport, stonehouse, all round the dock yard.
Places that are nice
Manamead, st Jude's, estover (ish), leigham, plymton, plymstock, roughbough, thornbury, anywhere that isn't near the centre of town