There are a number of bars and cafe bars in Krabi town center that cater to tourists, expats and natives. A few of them will have live bands at the weekend belting out cover songs, though Rocky Bar has live music every night. Stick to the main areas and it is most unlikely you will have anything but a pleasant time.
The Roof Top Bar above KR Mansion next to the 7 eleven on Chao Fa Road is an option. Its a good place to watch the sunset and have a cocktail.