We have been to St Augustine several times and stayed in different types of accommodation, so it depends what you are looking for.
We have stayed at a B&B called At Journey's End. This was lovely, very short walk to all the main old town attractions and the nearest trolley stop (can highly recommend the old town trolley tour
). The couple who run it are fabukous, so friendly, and gave us lots of recommendations. The breakfast was not your usual run-of-the-mill American breakfast - the host is keen to offer you a slightly different breakfast experience. The room was lovely and the one we stayed in had its own verandah and a huge bathroom.
http://www.atjourneysend.com/
A couple of years ago we stayed at the Hilton Historic Bayfront. It was a Hilton but not as you'd know it. It had been carefully designed to remain in keeping with the surrounding area, so does not look or feel like a Hilton. Room was huge, customer service was great. The only downside was no self parking but the daily service charge included valet parking. Pool was a little small but we didn't have time to use it anyway. Again, very convenient for the old town, particularly George Street.
http://hiltonhistoricbayfront.com/
This year (next week) we are staying at the Casa Monica hotel. I have admired this hotel on every visit, it is so beautiful. I can't wait to stay there
http://www.casamonica.com/
I can let you know afterwards how it was if you like