I live outside Jax. Do you have children? You will have a car, that's good, you need it!
What I would recommend doing:
-Get out of downtown, I don't care for that area and it's dangerous at night. Nice hotels though but don't just walk around the city. Ruth Chris Steakhouse is downtown, a fab place to eat! Traffic in downtown is bad too.
-Hit St Augustine. It's about a 35 min drive down I-95. See the historic sites (Castillo de San Marco, St George Street, Flagler College), shop at antique shops and look at local art. Go see the St Augustine Lighthouse, if you have time, hit the Alligator Farm across the street from the lighthouse. Also, right near the lighthouse is Anastasia Island State Park. Prettiest beach in the whole area, wide white sand. Very clean. Beaches in Jax are not clean, they are fairly dirty in some areas.
-Go north up 95 (or take 9A) and get off at Hecksher Dr. Go to the zoo, or to Hueganot city park. (Beach) you can drive on the beach there. Keep going up Hecksher to Amelia Island. Amelia Island is beautiful!! Big and Little Talbot Island are very pretty--go kayaking at the state park there (Talbot Island state park--company that rents them is called Kayak Amelia). Go to Fernandina Beach--very neat little old town, cool places to eat and shop. Lots of Bed and Breakfasts too. Looks like old Florida. Love it!
-His the St John's Towne Center for shopping. It's an open-air mall off of JT Butler Blvd, near UNF. Cheesecake Factory, Sephora, lots of neat shops. The Avenues is a nice mall too, on Southside Blvd.
I can provide links if you want them, but that should get you started! Welcome to Jax!