Dog Breed and a certain weight will prevent you from renting a big sector of the rental market. Its just not worth their liability when someone without that liability can be rented to, and I dont blame them.
You may want to rent sight unseen before you arrive so you dont get here and find out theres nothing ACTUALLY available to move-into.
Every apartment building and even zillow and realtor.com site has listings for rentals that you can browse on your own. Theres really not much we can do on a forum. Its about you and your credit history and dogs that will dictate where you go. I dont see why most any apartment building wouldnt rent via online portal.
If you are going to be here anyway, sign a lease on the first place you come to that has availability and accepts the dog liability. Do a 6 month, and you can bail out even if it costs more.