The Zone Colonial is a very interesting place.
There is nice architecture and lots of old colonial buildings.
You can go to small little parks to sit down.
Calle El Conde
The Main Street is the Calle El Conde, where many painters will show and sell their work. Other than that it's just a street with many shops designated to tourists.
Make your way through the streets other streets to take in the flair of the Zone Colonial and see the many interesting buildings.
In my opinion it's very safe to walk all of Zone Colonial.
I'm not sure about the rest of Santo Domingo, many locals warned me, although I never felt really threatened.
Definitely book a tour with the Chu Chu train. The tour will last 30min and cost around 10$. They will tell stories in many languages about the Zone Colonial and you get a quick and good overview of the Area.
Remember the street names of the places which you liked, while on the train, and visit them afterwards by foot again.
See my highlights of the Zone Colonial also in my Map below.