Like to go shopping? Check out the St. Johns Town Center. This upscale open-air mall has over 175 restaurants & retailers including The Cheesecake Factory, P.F. Chang's Lush, Sephora, Banana Republic, Tiffany & Co. and so much more!
If you like to golf, then you should check out TopGolf while you're here. Food & drink menu is provided. They do take walk-ins, however, wait times can be long so it's easier if you reserve online.
Know for it's Spanish colonial architecture. St. Augustine is one of the oldest cities in the U.S. There are numerous things you can do while site seeing here. From going to museums, shopping, visiting the Castillo de San Marcos National Monument, etc. Depending on where you'll be staying at in Jacksonville. St. Augustine ranges from 30 to a little over 50 miles away from Jacksonville, so if you plan on visiting St. Augustine, make it a day trip.
Believe it or not. Jacksonville is still warm in October, so why not visit the beach while you're here. Jacksonville Beach has multiple restaurants & bars that you can check out as well.