The best way to get around the island is by car. You can rent a car at the airport, and for less than a taxi ride to and from Nicosia you can have a car for 4 days. A car is very handy since the island is fairly small and the roads are in fairly good condition. You're never more than an hour or two from the water, and almost the entire island is a day trip out of Nicosia. There is a bus system on the island, but then you're stuck with difficult schedules, and you still have to find your way from the airport to your hotel (even the closest Larnika hotel is an hours walk away). There are also no trains in all of Cyprus, so this is not an option.
Be warned that if you want to cross over to the North, most car rental insurance does not cover you. They will offer to sell you insurance on the other side, and that might be a good idea. If you get into an accident on the North side, and you don't have extra insurance you might be in trouble.
Later