An all inclusive resort works because you get all meals, most alcoholic beverages and access to beautiful private beaches, along with your room.
Ideally, you'd want to combine your stay with trips OUTSIDE of the resort so you can enjoy the local culture. As a solo traveler, the best way to do those outside will be to pair up or become part of group. Befriend people at the resort during the day so that you can go out in the afternoons or evenings. Dominican men in these resort towns are very aggressive and usually view women travelling by themselves as "in desperate need of companionship", intimate companionship. Avoid going on excursions organized by the hotel. Hire a driver and have him take you to spots. Drivers will wait for you and wait for you to drive you back for a fraction of what the hotel will charge you for those "excursions". As such, you will create your own excursions with much more flexiblity and tailored to you and your group.
Do your research about things to do and places to see BEFORE you arrive. There's enough online to create a nice itinerary. If that fails, check out a travel guide from your library or just buy it used.
Regarding your request for recommendation for hotels, please indicate your budget or how many stars you'd like. Be aware to deduct one start when comparing to hotels in the US. Example: a 4 start hotel in Punta Cana is truly a 3 start hotel in the US. The Westin Punta Cana is a nice one and well run. All I care is for clean places to sleep, since most of the time I'm at the beach or out exploring places outside the resort. Do a day trip to "Parque Nacional del Este". It's the DR's idea of a National park in terms of preservation.
DR is safe, especially towards tourists, but use common sense and don't overdo the jewelry and flashy items. Leave your iPhone at the hotel and travel light with just the money you expect to spend that night and ONE credit card. While on credit cards, on previous travels there my credit card has been cloned and I end up having to report it when I come back home and start seeing all the charges I didn't do. I now use a special travel credit card where I don't have any recurrent charges and I don't have to re-set when I report the card compromised.
A lot of the tourism staff, at hotel, drivers, at restaurants and cafes will speak some English but do what you can to learn at least a couple of words and phrases BEFORE you arrive. It shows respect and it will allow you to practice.
PM me if you'd like more info.