With the Dominican Republic being home to a player from just about every major baseball team, it should not be surprising that the national sport is "beisbol."  When the Red Sox won the penant in 2004, residents were wildly proud of the series Most Valuable Player, David Ortiz, who is from Santo Domingo. Pedro Martinez is another Sox teammate that hails from here. They even have their own Professional Winter League that plays at the Liga de Beisbol Stadium.

Horse racing is another favorite activity to be found in the city at Galapagos Hipodromo V Centenario. They have a restaurant and admission is free. With water, water everywhere, there's not a drop to waste. Go swimming on any number of pristine,  white-sanded beaches, or rent a jet-ski (though all waterized motor vehicles are forbidden during Easter week, due to the high volume of tourists). 

There are many parks in and around the city, such as Mirador del Sur Park, useful for jogging, biking, backpacking, and other outdoor sports. Every major resort will have a tennis court.

One-stop shopping for tickets in Santo Domingo, be it for sports, concerts, or theatre, is Ticket Company. Go there for an event calendar that will help you make your choices.