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I'd recommend nuclear.
Hardly surprising :lol:
Since I am pretty uneasy with operating nuclear powerplants in a tsunami region and without a backup power grid, I would recommend putting your eggs into multiple baskets.
Since you are close to the equator, covering every roof with solar arrays would be expensive, but very effective. Wind power should also be pretty reliable, you are right between the doldrums and the horse latitudes, so most of the time, you should have a pretty stable wind, sometimes just far too much wind.
Finally, as conventional backup power, I would use a triplet of combined cycle as turbine powerplants. Those can be made very small and reach extreme effectivities in practical use, a power plant in Germany reached 60.75 % thermal effectivity in 2011. Also, they are very agile and can be powered on or off in a matter of seconds.
This example is a 2x400 MW powerplant, much larger than you likely need for your spaceport:
Since you can build such a power plant really small, it is also no problem to spread them out, so they are not all in the same location during a disaster.
Since you also need to produce hydrogen at your spaceport as rocket fuel and store it, you are in a very lucky situation: You can use solar and wind power for producing much more hydrogen gas from the ocean than you actually need for your rockets and use the hydrogen gas for the CCGT power plants instead of natural gas, should you ever have a wind still night or very high temporary power demands during spaceflight operations.
With hydrogen all over the spaceport, you could also use fuel cell stacks as local emergency power supply instead of the classic Diesel generators.
Just remember the "two island principle": Never have everything your life depends on in one place, so it is very unlikely that a disaster will destroy both locations completely.
Finally: Using such a hydrogen-base regenerative infrastructure would also have the advantage, even a full "end of the world" style disaster (like a really really strong typhoon) would not have the risk that even a mild nuclear accident would contaminate your spaceport island and make it unusable for years.