Abodo.com thinks a great apartment should be easy to find, and offers a pet-friendly apartment filter in their easy-to-use filter.
ApartmentList.com enables you to find pet-friendly housing by checking the Pet Policy option from the Advanced tab at the top of the page, once you’re searching in the area you want to live.
My Apartment Map is a search tool that allows you to search by region and type of pet(s) you need them to allow.
National Apartment Locator Sites:

And once you’ve made your move… check these articles for information on making it a smooth transition for your pet(s):