The island of St. Croix actually only has the two cities: Frederiksted and Christiansted dividing the island roughly in half, so everyone has either a Frederiksted or Christiansted address. It was further broken down into nine "quarters" by the Danes when they ruled here. Then it is also further divided into 77 estates which date back to individual plantations back in the 1700 and 1800's. Most of our physical addresses (and mailing addresses for those who receive mail at their homes) are based on these. For instance, I live in Christiansted as my town and also Cotton Valley as my estate. My home address is "xxx Cotton Valley, Christiansted, VI", but I also live in "East End A" quarter. To make directions worse, the number part of your address doesn't tie to a particular road (I live on Sierra Verde Rd., not Cotton Valley as my address indicates), so we drive by directions (e.g. "head east, go past "xxx", turn at the blue house, up the hill you'll see a big mahogany tree, turn left, and...".
Sorry for the island geographic lesson first, but to answer your question, we tend to think of the island in areas. Sion Farm and Castle Coakey is where we shop for groceries and household goods. Beeston Hill has a great gym and physical therapy center, etc. For great places to visit while you are here, they are less tied to these "hamlets" or estates and more area based. East end of the island has Point Udall, the eastern most point in the US and an early morning gathering spot to be the first people in the US to see each day's sunrise. Also has good hiking and very private beaches (Jack and Issacs Bay). Other more accessible beaches that we enjoy on the east end are Chenay, Boiler Bay for snorkeling and privacy, and Shoys. Heading west is the historic town of Christiansted with the original dutch fort and buildings in town. Further west you'll hit Salt River which is the only spot in the current US that Columbus actually landed at. Salt River also has a bioluminescence bay you can kayak in and it is where the Cane Bay dive boat leaves from. Further west is Cane Bay which has great beach side eating and good shore diving and snorkeling. Finally you hit Frederiksted for the Pier, more good shore diving, and Sandy Point (the best beach on the island for sand and water quality). The interior of the island is mostly agriculture and commercial. The south side is dominated by the Captain Morgan refinery and the giant oil refinery that dominate the skyline.