It'll be hard to find a whole house to rent (although I've seen a few in the Hydrostone neighbourhood, for around 1,500).
You should be able to find an apartment or condo at that price though, either in a purpose-built building or one storey of a converted house, like this (which, I must add, looks really nice and unusually cheap--these are normally a few hundred more):
http://www.padmapper.com/show.php?source=5&id=239708709&src=main
If you're looking in the North End and West End, house prices might be between 350k to 450k for three-bedrooms in decent shape. If you consider downtown Dartmouth you're still pretty central and can knock 50k off that.