I was just in the D.R. in March, was in La Romana and Sto. Domingo. Now's a great time to go, they're having serious inflation problems which means things are cheap for anybody with dollars.
My Mom worked there as a nurse for an organization called CARE way back in the 70's and has been going there almost every year since '98, so we know quite a few locals. Since my parents are both nurses, they do some humanitarian work in addition to going there to relax. There are a lot of really nice people down there, and most of them don't have any problem with Americans as long as you're careful not to fulfill the obnoxious tourist stereotype. Kinda sad things are so messy down there.
As for Sto. Domingo itself, I think one of the neatest places to visit is the historic city. Don't miss the cathedral, and Diego Calogn's (don't ask me if I spelled that right) house is interesting as well. One thing I do wish is that they would keep things cleaner, as it is, you can't really explore the historic district without running into some litter, animal droppings, and things like that to remind you of where you are. Overall, it is very nice though, and I'm glad you're willing to do something more than kill time at the resort.
Oh, and I don't claim to know all about cigars, but I've learned a few things. First is that you're still going to pay a pretty penny for the big-name cigars (red dot Cohibas, H. Upmann, Romeo and Juliet, Punch, etc.), unless you're better at finding these things than we've been, and if they're cheap there's a good chance they're fake. That being said, there are a lot of pretty good off-brand cigars to be found for a fraction of the cost. We've even bought bulk packs that were supposedly rejects of some kind from some of the shops that weren't bad at all. Of course they're not as good as one of the names mentioned above, but methinks you'll still enjoy them if you're not too picky. Oh, and it seems like everyone has their own "Cohiba" (some info
here), and it's probably nothing special if it isn't a red dot. More info on counterfit cigars
here. Also, many of the well-known Dominican names are produced in free-trade zones, making them illegal to sell in the D.R.. So, I would suggest that you be careful if you go brand shopping, and look out for fakes. I'd also recommend you try out some of the off-brands found at the independant shops; some aren't much good of course, but others are a great deal.
Enjoy.