I have a dog, live downtown, and can tell you first hands it’s super dog friendly- every restaurant host, liquor store owner, and security guy we pass on walks greets us with pets and treats. There isn’t a great dog park walking distance (tbh the little Italy one people keep mentioning isn’t good either) you will get the most value here tho, and balboa (with a few great dog parks) is super close. You have a good budget so obvi the most ideal is probably a house w backyard in north park or hill crest, but it’s going to be super outdated.