We have been visiting St. Augustine for well over 40 years and now own a condo over on Anastasia island. Parking can be a nightmare so you picked a good place to stay if walking isnt a problem. There is a multi-level parking garage right next to the Visitors Ctr. (lots of good info in there) off W. Castillo Drive if you need it.
For sure walk around the old colonial part of town (St. George St...), it's pretty much all pedestrian traffic only. There are lots of shops, restaurants and bars in that area. A tour of Flagler College is nice, they occupy a large portion of downtown. Walk across to the Castillo San Marcos (the fort) and along the break wall there. The Alligator farm is good if you like reptiles (there are much more than just alligators there). Take a drive across the Bridge of Lions over to St. Augustine Beach. Park in one of the beach parking lots -a good one is by The World Famous Oasis Restaurant at Ocean Trace Rd. (our timeshare is down there by the beach) and walk on the beautiful wide beach. There are some nice restaurants right by the beach if you want a view while you eat. They are The Beachcomber on A Street at the beach in St. Augustine Beach or up at the north end of town take the bridge to Vilano Beach and go up to Aunt Kates (on the intercoastal) or The Reef on the ocean, or there is The Beaches at Vilano restaurant on the intercostal by the old bridge & boat ramp, almost under the new bridge.
Enjoy St. Augustine, we'll be back there March 5th! Cant wait!
~Diane