If there's 2 things that are very characteristic of Baní, that's mangoes and dulce de leche. Baní provides the best mangoes of the country, and they even organize a mango festival every 2 years in June. In all food stands on the roads you'll see several kinds of mangoes, so don't hesitate to haggle to get them at a good price. Another thing you'll see is mango trees all over, but be careful not to take the mangoes from a tree inside a house.
Dulce de leche is another thing that's from Baní. The best stores to buy it are Las Marías, Las 3 Rosas and El Húngaro, all of them in a little town called Paya - between Baní and San Cristóbal but any dulce de leche from Baní is just as good.
However, our dulce de leche isn't like the ones on the Wikipedia article. Ours are solid and sold "in paste". If the paste then is cylindrical and covered with yagua (a kind of palm "Attalea humbolddtiana") then it's called raspadura. We also make dulce de leche with various marmalade fillings: orange, guava, figs...
On the road Las Dunas - Las Salinas, you'll find what the locals call "salao" (or salado). That's a piece of terrain where sea water comes to land and stays there for a certain amount of time. It's not too much water that will flood the area, tho, but to avoid the sea water going farther than it should (read, inside people's houses), they have aligned some stones.
At the salt mine, the workers use salaos to produce big grains of salt that will then be sent to refineries to process for human consumption.
It is forbidden by law to take one of those raw grains of salt and take it out of the country, as well as use it in food preparation.