Not too familiar with the Hard Rock there.. but I am very familiar with Punta Cana..
First thing's first...
Bring your own!
Outrageous resort area prices on sticks.. I am not aware of any place within miles of Punta Cana where sticks can be had at reasonable prices..
Tons of smoking options in the area though.. Cigars are part of the local culture... you wont have any problem finding places to smoke..
La Romana is about a 45 minute to an hour drive from Punta Cana (depending on traffic, weather, etc..).. and is where La Flor Dominicana and other companies have factories.... you can do tours on your own (just show up.. most of the factories do regular tours throughout the day).. or you can link up with a tour company that will take you to several "cigar" destinations for a pretty reasonable price..