Travel To House Sit?

That sounds like it would be fun for you but I'm not sure how owners would find you since they search by location/zipcode. Also many owners want to meet with potential sitters before. They'll contact more than one and select the one they like best. Certainly you could talk with the owners from wherever you are, even do FT (or similar), but that may not be enough to provide the assurance they need for you to be in their home. Finally, many owners might prefer to have a local sitter for those last-minute occasions or short periods of time when they need someone to take care of their pet.

You'd probably be better off getting yourself bonded and insured and then advertising home/pet sitting services on CL in the city you want to visit.

Add: I believe there are other petsitting websites in which owners post "help wanted" type listings, which you could answer from anywhere in the US. However, Rover's customers do not place those types of listings.