Flying to the US Virgin Islands is relatively easy. Delta Airlines offers daily non-stop service to St. Thomas via Atlanta, and both St. Thomas and St. Croix can be reached by Jet Blue, American, and others via San Juan, Puerto Rico. Visitors to St. John will need to fly to St. Thomas and take a ferry across to Cruz Bay.
If one is going to the St. Thomas Airport or St. John, Delta or American is definitely the way to go. The airport at San Juan can be a bit difficult, especially when changing planes, so even visitors to St. Croix may want to consider flying direct to St. Thomas and shuttling to the St. Croix Airport from there.