I don't know anything about the resort, but I do know the island very well as I lived there for many years.

The Albany is on the lea side of the island. I took a quick peek at the pictures and there's a reason you're not seeing much in the way of beach photos. This is one of the later parts of the island to have planned tourist development.

You could certainly drive to Paradise Island for the evening, if you don't mind driving through the back roads of Nassau. A quick look at GoogleMaps show it to be about 25 km point to point and 35 mins driving time. I don't know why you couldn't take a boat around the island, in daylight, if you were familiar with the surrounding ocean. It's not something I would do at night.

I hope that's useful.