In Nassau, Cruiseradio.net lists a few places for free WiFi:
Regarding Festival Place, I was there recently on a Carnival cruise, which stays overnight in Nassau. As I was walking to Senor Frog's at 10PM, there were about 40 people sitting outside the entrance to the building, all lit by the glows from their iPads and laptops. It was really creepy, actually.
"1. Festival Place: Right when you get off the cruise ship, go to the center of the shopping plaza (you have to walk through it to leave) and you can grab some free WiFi. This is one of the most popular spots so dont expect top speed.
2. Dunkin Donuts: Located right off of Bay Street, a lot of crew members go here to Skype and call home because of the strong bandwidth.
3. Conch Fritters: You cant go to Nassau without getting seafood or conch fritters, right? You can expect to pay about $10 a plate for some local seafood and you can jump on the free WiFi, too. Located off Blue Hill Road in Nassau. All the locals can direct you to this popular venue.
4. McDonalds: Located on West Bay Street, just a short walking distance from the cruise pier. This is pretty much standard at all McDonalds.
5. Cable Beach Casino: If you want to spend the day at Cable Beach and soak up the sun, you can grab some free wireless in the lobby of Cable Beach Casino."