I just found a place that thankfully allows one cat, and is not crazy expensive either! I did, however, have to pay one months’ rent as the pet deposit in addition to the standard damage deposit, so that ended up being a bit expensive - but my cat is a good boy, so I was more than happy to find somewhere that’s affordable AND pet friendly.
Sorry I don’t have any advice for dog friendly places, but it never hurts to be up front about it and ask if they would consider it - especially if your pup has good references too!