You can definitely rent a car fairly easily from one of the hotels on that beach if not from the Occidental. I'm not sure what company is in that hotel. Each one seems to have one. I'm not sure about prices vs the price at the airport.

How long are you going to rent for? If it's for the duration of your stay, you're probably better off just renting at the airport. When you exit the airport, there are several rental places right across the street. If you reserve ahead of time, it's about a 15 minute process.

Btw, if you're planning on driving off-road, most of the rental car companies don't allow it, and cars do break down/get flat tires out there. If you're just going to restaurants or into Oranjestad, taxis are very easy to get from the hotel. The main reason to get a one day rental would be to go to the light house or to Baby beach.