Go to the city park Hanna Park-it has a beach and showers restroom facilities. Its on the Southside of town.
Shopping is the best thing to do in Jacksonville. The downtown riverwalk is overpriced. The Hilton hotel downtown has a great lunch buffet.
The zoo is nice. There is no aquarium. Museum is ok.
A nice area to walk around in that has a park is the Riverside section of the city. It has a lot of old FL homes. Free parks and nice restaurants. Also the San Marco section of the city has many nice old FL homes and nice restaurants.
But if you want to stay on the Northside-thats where the cruise port is- there''s only the zoo, eating, shopping. You can also go to the ocean on the same road where the cruise port is-they are called the jettys by the locals.