I live here and there are no safety issues - especially in the Dockyard and Hamilton and St.George. For a first timer I would strongly recommend you hunt down a "Blue Flag" tour taxi. These are certified tour guides and do a great job. The cabs are usually mini-bus size and doing the tour with another couple or two spreads the cost. You might consider asking for a 1/2 day tour that ends up dropping you in St.George at the other end of the island from the Dockyard. You can then take the fast ferry directly back to the ship. Again 6 people will spread the cost and probably make it more fun. If you like to be independent and have an interest in laid back and tranquil, get the first ferry in the a.m. from the dockyard to St.George. The ferry ride is great and St.George is a historic gem where you can take walking tours or self-guide. There are also a couple of beaches and old fort sites nearby. To get back to the ship at dockyard you can either ride the ferry or take the bus back to Hamilton (in the centre of the island) and then take the fast ferry from there back to the ship. Depending how much time you decide to spend in St.George the bus option also gives you the opportunity to stop at a couple of other attractions on the way back to Hamilton: The Crystal Caves and the Bermuda Aquarium in Flatts Village. The best deal for travel is to get a 2 day bus/ferry pass. These may be available on-board. The other option to all this is to rent scooters and just go see the place! You cant get too lost and anyone can point you back to where you need to go. Enjoy your visit!