St. Augustine is a beautiful old city (oldest city in U.S.) I lived there in the 1970's and moved away like a big dummy..lol... The city of old St Augustine is still about the same, not changed much at all. Across the river is St Augustine Beach on hwy A1A, that area has completely changed since the 70's. Pets are allowed on some of the beaches as long as they are kept on a leash. I moved back to FL in 1993 and stayed til 2006, lived two hours south of St Augustine, we made several trips a year up to spend weekends there. My wife and I both really like the town a lot, if we ever move back to FL St Augustine is it. Here is a link that may help you out, on the left side of the page are several links that may answer a lot of questions for you.
St Augustine Florida Information