We're moving to the area soon too and I've been looking at rentals as well, although not in Salem. In general we've found that apartments are pretty pet-friendly. Here are a couple of links I've used in my searches.
This is an organization listing most of the apts/property managers in the area:
RVAA Roanoke Valley Apartment Association Official Members
This one is the local paper's rental search (you can search by pet-friendliness):
Apartments and Rentals in Roanoke
This last one is the online version of the free apartment guide that's found all over town. It lists apts by area & has pet-friendliness listed.
A Guide to Apartments - Roanoke Valley Apartment Guide
I hope this helps --- we just returned from our first in-person visit and are happy to report that the apartments we checked out were as nice as their ads described them. I hope that's the case for you as well.