The place where I'm now staying is in the Zona Colonial (the old colonial part of town). It's near the coast, near the port where I arrived. I've seen a number of the architectural marvels. Today I plan to go out and walk around some more. I'm not generally the most interested in this type of sightseeing, but in certain circumstances I like it. Here, in the first European city in the New World, where Christopher Colombus, Hernan Cortez, and others walked, I find it particularly appealing.
In addition to the fascinating historical buildings, there are of course tons of touristy gift shops, restaurants, etc. Personally I don't find those that appealing, but I guess that some people do, and I can kind of see the appeal. Still, for food and other purchases, I often prefer to try the authentic local stuff, i.e. the stuff that doesn't say "authentic" in the marketing materials.
I've just been reading some local information provided by the Airbnb hosts, including a pamphlet in French. I've seen a number of other visitors around the old part of town, including some French-speaking tourists.
Santo Domingo does have beautiful architecture. In general I like Latin architecture (along with food, music, etc.). I think the culture has an aesthetic quality that resonates with me. Do you have any favorite cultures?