At this moment, I wouldn`t invest in the DR specially not in Pesos, neither Us Dollars. If I were you I would invest the money in the USA, Panama or Bahamas, but you may not gain the same interest rate. Although, your money will be secure and SAFE from bank`s frauds.
If you really need to invest in the DR (to gain the attractive interest rate), I would recomend you:
Banco Popular. They are the biggest Dominican bank, and one of the most conservative. They also own an offshore bank, which might be interesting for your investments.
BHD. They seem to be a stable bank.
Progreso. Owned by one of the richest Dominican families, they represent American Express in the D.R.
Banco Leon. Although it is a new bank, result from the Bancredito Fraud, it is now backed by the Leon Jimenes group, owners of Cerveza Presidente and Marlboro.