A lovely apartment in a good location. There is one snag which I'll explain next, and then I will tell you more about the apartment and environs.
Recently (early 2018) a restaurant opened just across the road. There is some noise from this. Firstly, there are two large kitchen extractor fans on the roof directly opposite. These make a drone from when they are switched on about 9am. It's about as loud as the sound of the surf. So, not dreadful, but a bit annoying. (We understand that they intend to install acoustic baffles, so it may be better in future.) The second source of noise is delivery and service lorries. There are only two or three of these a day, but they tend to park just below and leave their engines running. Note that when we were there, there was no music or other loud noise from the restaurant, and we had no trouble at all sleeping at night. (Though we were woken a couple of times by early morning garbage pickup.)
The apartment itself is lovely and light and airy. There's air-conditioning throughout, but we just opened windows front and back and enjoyed the though-breeze. The kitchen is well equipped the living area comfortable, and there are lots of useful extra things (beach chairs, etc etc). The mosquito net in the bedroom is excellent.
We have stayed in the same apartment block before, and know the area pretty well. There is a nice beach just across the road (there is some traffic on this, but nobody would describe it as "busy".) This is very quiet --- we seldom have had anyone else swimming at the same time as us. There are shoals of fish and even the occasional turtle to see just there. (If you are going to snorkel here you should use a dive float to make sure the jet-skis see you.)
Speightstown itself has restaurants and shops if that's what you are looking for. In particular if you really want to self-cater like us, you can find almost everything you'll want at Eddies and Jordans, which are both a few minutes away. The town is also near to other nice beaches on the west coast. (When we were there in February 2018 the sargassum on the east coast was still a problem, so you will want to visit the east coast, but probably not swim.)