Port Lucaya is the more vibrant part of Grand Bahama Island for tourists. This is where you'll find restaurants, bars, and shops that tend to stay open later. There are also at least 5-6 hotels right in the proximity of one another, shops, a marina, and a casino.
We found ourselves watching small striped fish as we enjoyed the warm breezes by the marina. The shops are almost the exact same ones that are/were in International Bazaar and have straw markets on both ends.
If you're staying in the Lucaya area of Grand Bahama Island (and even if you're not), the Port Lucaya Marketplace is a nice, clean, hoppin' spot. There are several pubs, cafes, restaurants of various styles and price ranges, and lots of shopping. Vendors include jewelry, perfume, souvenirs, and the stuff typical of cruise ship ports of call. Within the complex is at least one small internet cafe. There are also hair braiders and independent market vendors to bargain with. If you want to do any water excursions, this is the place many of them depart from.
Lucaya is the only place on the island to go shopping. The area has quite a few shops so it will keep you busy for a little while.
Port Lucaya has something for just about everyone. Shopping, restaurants, souvenirs, live events, boat trips, bars, banks and the casino.
Shopping and eating at the Lucayan Center is ok, too. It was a long couple blocks walk from the bus stop. There were also docks there where you could charter trips out of---I think.