Yes, there are. However, since most people visit Jamaica for the island's breathtaking natural beauty - the beaches, mountains, waterfalls, etc.- most of the activities are outdoors.
I am unsure where on the island you plan on staying, so the following outdoor activities in Jamaica are grouped according to city/ town.
Cocojam - A game arcade and indoor playspace for toddlers.
Bob Marley Museum- An indoor museum focused on the life of the famous musician.
Devon House- This historical tour educates people about life in 18th century Jamaica with a famous ice cream shop on site - suitable for kids and adults.
Rose Hall Great House- A historical tour of a haunted house.
The Hip Strip- A busy commercial strip in the heart of downtown Montego Bay where indoor art galleries and restaurants abound.
Ricks Café- This is a cool bar and restaurant with good music, the best sunset views in the island and good vibes. Also known for extreme diving from outdoor cliffs if you venture outside.
Appleton Estate Rum Factory Tour- A fascinating tour of the rum making process. The factory is technically located on Jamaica's south coast (in the parish of St. Elizabeth) which is a manageable distance away from both Negril and Montego Bay by car.