Paul--
We recently (last month) did alot of travelling in DR and here is what we found:
1) The Banco Popular and InterBan and their like generally are bad places to try to cash travelers' checks. Most of the time the staff looked blankly at us and told us they couldn't do it.
2) Money exchange houses other than banks wanted to charge alot more for changing our travelers' checks, and due to the law that restricts which entities can change currencies, we stayed away from them. Dominican law is pretty strict on this point, so if you are uncertain as to whether any business (bank, exchange, hotel, restaurant, etc.) has authority to change currency, walk away and don't chance getting in trouble with the law.
3) The best place we found for changing travelers' checks was our hotels. No hassle, great rates.
4) Unless you're planning to shop at touristy shops near Santo Domingo (Boca Chica qualifies), you probably will need Dominican pesos. Use of credit cards is expanding in DR, but unless you're at a resort or tourist shop, bring pesos.
Hope you enjoy your trip! Susan