The National Botanical Garden (Av. República de Colombia, 9 a.m.–6 p.m. daily, RD$30) is a lush and expansive display of many different kinds of plants—aquatics, orchids, bromeliads, a bamboo garden, many kinds of trees, and even a Japanese garden. This botanical garden is well taken care of, and there is a trolley (RD$15) that you can catch every 30 minutes. It drives you around and you hear explanations of the different areas in many languages.
It is wonderful to enjoy the shady grounds and serenity, which you can’t find in many places in the very frenetic Santo Domingo [1].
While there, visit the Museo Ecológico (9 a.m.–4 p.m. daily, US$0.35), which has encased displays of the many ecosystems of the Dominican Republic [2], including the deserts, mangroves, mountains, and beaches. This portion is air-conditioned. Children might enjoy this park, if only for the trolley (it looks like a little train) and the wide open spaces for running.
Links:
[1] http://www.moon.com/destinations/dominican-republic/santo-domingo
[2] http://www.moon.com/destinations/dominican-republic