Well, Punta Cana doesn't have many options.
There's the Hard Rock Cafe at Palma Real Shopping Center.
Also Mangu Disco that has international music at the ground floor and electronic at the second floor.
If you like Dominican music Areito plays a little bit of it plus international music. I particularly don't like this place too much because their music is usually old (I'm not talking about oldies but like last season music, the dj needs an update badly)
If you just want to relax in a chill out place at the beach Soles Bar at Los Corales and Jelly Fish are the places to go, they're both restaurants/chill out bars.
There's a bar that's only open during the weekends, the name is Hot Spot, it's located in a cave, fair prices and the owners are awesome (you might see some pics of me if you go there

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All these places are located in Bavaro.
At Punta Cana I only know Mascara Bar, it's located at the Punta Cana Mall, right where the bowling alley is. If you go there ask for David, he's in charge of it. I like it.