Nuclear

Micro nuclear plants, like this one from Toshiba: Toshiba 10MW nuclear plant

Pebble Bed Reactor, safer, simpler and more efficient type of fission reactor. At least one prototype currently operating.

Disadvantages

Although nuclear power has a lot of advantages, we need to keep in mind that Seastead will have to be near existing countries, at least in the beginning. Countries probably don't mind a cruise ship kind of operation in their vincinity, but both governments and the public will mind a vessel carrying "scary stuff" and take appropriate action. Although nuclear options may be very cheap and eco-friendly, it is probably better suited for spaceships instead of humble seasteads.

There are many more ways to get energy, and Seastead is an extremely good place to experiment with alternative energy sources like algae since "land" can be made easy. To get things going, focussing on technology that is easy to obtain and to use is probably the best and only way to go.