Haven't stayed at the Divi, but have toured it and a few other resorts in the low-rise area. Best recollection is that the Alhambra Casino is within walking distance, but nothing much else as far as night life. You would have to go into town (a couple of miles) or the high-rise section (again a couple of miles). I do believe that each hotel has some entertainment most nights of the week. It all depends what you are looking for.
Good luck, and enjoy your stay. We will be returning in Dec. for our 8th visit in 7 years.