Most historical sites in Santo Domingo [1] are within the Ciudad Colonial [2] (Colonial City). Churches, homes, the first European fortress in the western hemisphere, and other colonial-era buildings are all within walking distance of one another, although you could always flag down a horse-drawn carriage if you need a break from walking.
In the greater Santo Domingo area there are many other sights worth visiting, such as the expansive Jardín Botánico Nacional [3] (National Botanical Garden); the Faro a Colón [4] (Lighthouse of Columbus), where the remains of the explorer are said to be laid to rest; and the Plaza de la Cultura’s Museo del Hombre Dominicano [5] (Museum of the Dominican Man), which features an impressive display of Taíno artifacts.
Links:
[1] http://www.moon.com/destinations/dominican-republic/santo-domingo
[2] http://www.moon.com/destinations/dominican-republic/santo-domingo/sights/ciudad-colonial
[3] http://www.moon.com/destinations/dominican-republic/santo-domingo/sights/arroyo-hondo/jardin-botanico-nacional
[4] http://www.moon.com/destinations/dominican-republic/santo-domingo/sights/parque-mirador-del-este/faro-colon
[5] http://www.moon.com/destinations/dominican-republic/santo-domingo/sights/central-santo-domingo/plaza-de-la-cultura