Hello
1) check
new hampshire apts/housing for rent classifieds - craigslist for apartments. (Keep in mind that many posts are made by the real estate agent handling the property, and this *should* be noted in each post whether they are the owner or the agent. )
2) get in touch with a licensed real estate agent who knows the area to get a list of all available properties.
Most property owners will want to run a credit check on all adults who will be living there, and you may have trouble finding a place that will accept the kitties (but it will be WAY easier than trying to find a place that will allow a dog!) Start your search early and check back often