It is HOT and HUMID usually in June. Rain showers are short and few. By hot mean in the high 80s up to around 91F.
The Dominican Republic is a big country. Say where you will be traveling, and recommendations for shopping can be made.
You may also go ahead and browse through our travel destinations for some advance info on the subject of shopping in each area. See
Dominican Republic Travel Information
Since you are posting in the East Coast, will in the meantime assume you will be traveling to the Punta Cana area. The Punta Cana area is also a big area. The best shopping area right now is at the Palma Real Villas Shopping Village, adjacent to the Melia resort, and its Cocotal golf course and Palma Real residential area. Further south is the Punta Cana Village, also with shopping and dining in very pleasant surroundings.
For more on shopping in Punta Cana, check out the Welcome Punta Cana guide.
See
http://dr1.com/travel/puntacana/welcome/index.html