I myself had a pet hotel some years ago!
I started advertising on Craigslist and Nextdoor and then I would tell all my friends to tell their friends at the dog park. I had cheap business cards made and I would give them out at the dog park or leave at the pin up board.
I used a free website making service called weebly and made my own website,
where I posted my LLC license, my state license, my pet CPR license, and photos of my hotel and my huge yard, with testimonials and photos. I would emphasize how my hotel and yard is dog proofed and just showed how i went extra mile to make my home safe and secure for potential boarders.
I was also on Rover, making sure all potential clients see how my yard is bigger than anyone's yard in my neighborhood, and how i am home full time so i can watch the dogs 24 seven.
Basically I would "brag" about all the good services I was offering.
Competition is very big, so you need things that will make you stand out.
Advertising on Craigslist with a link to my website was extremely successful.
Nextdoor was good too.
I would always make sure to describe all those things were i went above and beyond for potential clients - like early drop offs, late pick ups etc.
My own dog was trained in 2 languages and sign language for obedience, and was 1 step away from K9 good citizen. So I see you are training dogs too, and that will definitely help you bring business in.
Good luck!!!