When I lived there, we would put the bags on our backs and take the scooters to play. It was a 45 minute drive up to Mid Ocean and Tuckers Point from Somerset.
Mid Ocean is without question the classic must play with some fantastic greens. Every hole has some sort of interest for the most part. The opening hole is a really fun to start with and it continues throughout.
I am too biased to have anything but love for Port Royal, but there are a few down holes early in the round. If for no other reason you have to see the 16th hole there.
After those two I would play Riddles Bay before Tuckers Point as TP is outrageously expensive. Plus I enjoy very much several holes at Riddles Bay. I never played the Belmont course before the renovation, but really wouldn't take the time to go back as it is quite tight and mostly uninteresting.
Before I left Bermuda, St. Georges was closed for the renovation, I would love to know where that went. It had some truly aweful holes with nets, out of bounds. It was a fun round in many ways though.
Oceanview is another publicly owned course along with Port Royal and, before it was sold, St. Georges. Not unlike several of the others, it is good golf in that you are in Bermuda and not much more.
The Southampton par three is a fun thing to do if you wanted to sneak it in after a round at Port Royal or Riddles Bay, if on that end of the island.
If I had only two rounds to play, one would have to be at MOC, the other would certainly be at Port Royal. Given three, I guess it would depend on where on the island I was staying. If in Hamilton, I would go back to Port Royal, if closer to the airport, it would be MOC.