Since most travelers come to the Southeast [1] to hang out in all-inclusive resorts, there are countless opportunities to book an organized tour at the excursion desks located in resort lobbies. All have comparable prices, and many are not included in the cost of your all-inclusive vacation, so be very careful when booking your sport or excursion.
As soon as you arrive to your resort, look through the offerings and book your choice, since these typically fill up quickly. Popular excursions include boat trips to Isla Saona [2] or catamaran rides, adrenaline pumping zipline adventures, booze-infused safari excursions, boat trips through the mangroves, and cave exploring in the Parque Nacional Los Haitises [3], to name a few.
Golf is a massively popular sport that has enjoyed much success in this region, with courses designed by Pete Dye, Jack Nicklaus, and Nick Faldo. The Southeast has the widest variety of top-ranked and world-renowned courses in the country, making it the best destination for the golf aficionado. While you can certainly bring your own clubs on the airplane, renting equipment at the courses for an additional cost is also a possibility.
Diving and snorkeling trips are popular off the coasts of Islas Saona [2] and Catalina [5]. Independent diving outfitters (as well as hotel dive organizers) arrange transportation for visits to these locations, along with rental equipment (make sure of the cost), and sometimes provide lunch or snacks. You will see coral formations, drop-offs, schools of fish, and even wrecks like the St. George or the Embassy. Diving in the converging waters of the Atlantic and the Caribbean (near Punta Cana [6]) can be a bit choppy with many currents and is not recommended for the beginner.
Deep-sea fishing, while not a top pick among visitors, can be arranged at most resort excursion desks. In the southern coastal town of Boca de Yuma [7], there are fishing boats lining the shore. Although there is nothing by way of a tourist infrastructure in this town, it is possible to hire a local fishing boat captain to take you out. Always ask about the experience of the captain and crew, and make sure that the charter has life vests, safety equipment, a working radio, and a license.
Links:
[1] http://www.moon.com/destinations/dominican-republic/the-southeast
[2] http://www.moon.com/destinations/dominican-republic/the-southeast/bayahibe/sights/isla-saona
[3] http://www.moon.com/destinations/dominican-republic/the-southeast/la-costa-esmeralda/parque-nacional-los-haitises
[4] http://www.moon.com/destinations/dominican-republic/the-north-coast/sosua/recreation/diving-and-snorkeling
[5] http://www.moon.com/destinations/dominican-republic/the-southeast/la-romana/sights/isla-catalina
[6] http://www.moon.com/destinations/dominican-republic/the-southeast/punta-cana-and-bavaro
[7] http://www.moon.com/destinations/dominican-republic/the-southeast/boca-de-yuma