Renting a car outside the US can be a risky proposition.
First, this isn't Avis, Hertz, etc. Thcar will probably be old & more likely than not will have mechanical problems. Tow service is unreliable at best. There is no AAA.
Second, you are probably NOT insured to drive there & will have to get additional coverage.
Third, if you don't really know where you are going, it is not safe. Not all road signs are created equal. How will you know a good neighborhood from a bad one?
The beaches by taxi are probably your cheapest venues. In St. Thomas we rode the cable car up the hill to the scenic overlook. The view was lovely but not really worth the price. You can go into town & shop. It's not exactly economical but I understand the waterfall in Dominica is not to be missed. We took the very expensive whale & dolphin watch but didn't see any whales.
If you want to see dolphins, get up very early as you are pulling into Dominica. The dolphins will be playing in the ship's wake.