Dominican Republic is a pretty stable country. The exchange rate when I lived there was about 3:1 and we lived quite comfortably. Crime is fairly low compared to Puerto Rico. Sosua and Puerta Plata have become quite tourist focused over the years with flights directly into Puerta Plata. Atlantic beaches are okay, a little bit rough. The capital of, Santo Domingo is about five hours.
That city is laid out pretty well with four major N/S streets and 2 major E/W streets. To get around the city you simply wait for a Publico or a public taxi. They are independent people with cars in various conditions but you can get around for about fifty cents. They load them up though. We had 11 people in an old Chevy Caprice.
Dominicans are warms and engaging and are very industrious when it comes to using what is available. Whether it is space, food, or accomodations.
Sightseeing, best on the south and east end of the country.
As you may know DR shares the island of Hispaniola with Haiti.
Yep, 90 days is all you get unless you apply for another visa of some sort. I overstayed my welcome by 30 days and when at the airport they wanted to send me back downtown, with my wife and kids ready to board a plane I found a way to get through customs and make my plane with a smile and some green.
I don't think you are going to move there. Remember Spanish is the local language even though in the tourist areas there will be plenty of English speakers. Plan a trip and visit before you decide to move.