Within walking distance, I would recommend La Cena (dinner only), Chew, and Burrito Gallery. La Cena is upscale Italian (with excellent fresh pastas). Chew is sort-of fine dining, new American cuisine; and Burrito Gallery is a burrito place - but its good and reasonable.
If you can drive, Orsay (Avondale neighborhood) is one of my favorite restaurant in town right now. Excellent food with french influences and great atmosphere. It's less than ten minutes from the Hyatt. Taverna (San Marco neighborhood) is also a very good kind of upscale place with mediteranean influences.
21 E Adams St, Jacksonville, FL 32202
agree with all the suggestions given, but would also add Bistro Aix in San Marco, and 13 Gypsies- very good tapas place. 13 gyspies is tiny, must have a reservation.
1440 San Marco Blvd, Jacksonville, FL 32207
San Marcos Restaurant
3351 17th St, Sarasota, FL 34235
We spent the night, last night, at the Hyatt and walked to Chew for a fabulous dinner.
The food was really great (you can see their menu online). The wine list is very nice--international and the wines available by the glass seem to cover all the necessary bases. I opted for a French Pinot Gris with Tile fish that was perfectly cooked.
We also had the short ribs--perfectly rich and beefy.
Love the gnocchi--not too heavy not too light.
The pasta carbonara may have been the best dish of all. Very tasty,
I would, absolutely go back.