Hi Fred,
There are a good number of pet-friendly hotels throughout the country. I’ve had luck with this website, which has an extensive listing:
http://www.pettravel.com
As far as short term rentals, that’s a bit trickier as each owner or management company will have different rules. In my personal experience I haven’t had any problem finding a place. I have a standard poodle and a Havanese. I would suggest finding a place first, then contacting the owner/agent about their pet policy.