Malé is small enough to walk around in an hour, and almost all sights are concentrated on the north shore, within a 15-min walk from airport ferry jetty.
Public transportation in Malé is limited to roving taxis, there are also ferries from the new terminal next to Jetty to the new Hulhumale development.
There is a small artificial beach on the east coast, about a ten-minute stroll from the airport ferry. It's not much compared to other beaches on the Maldives, especially as most locals bathe fully clothed, but there is some excellent surfing if you're experienced enough.