I have teenage grandsons that come to visit. They LOVE to stay at the Hard Rock, so you might consider that hotel.
Don't know if your boys are into skateboarding, but if they are, there is a great skate board park about 6 minutes from the Hard Rock. Let me know if that's something of interest and I'll give you directions. (They rent out skateboards).
The Molly Ringwalds will be entertaining at the IP casino resort (about 4 minute drive from Hard Rock), on Dec. 31st. If your here on the date, I think the boys will enjoy the show. There is a Christmas show "Spirit of Christmas" at Beau Rivage Dec. 17 to Dec. 27. I think the tickets are around $9. I'm not sure that's something that would appeal to the boys, but maybe. You can look it up on the Bea Rivage website.
I would certainly take them to "The Shed" in Ocean Springs for some really good ribs. It's a bit of a drive, about 25 minutes but well worth it. You can google it. Unfortunately all the water toys (jet skis, boats etc.) are not available for rental this time of year, but the beach is still beautiful. It was in 70's yesterday but today in the 60's. You never know around here if it's going to be warm or cold in Dec. as the weather changes back an forth almost daily. I just remembered something the boys will certainly think is very cool. There is a laser and christmas light show with music both Christmas and Rock at a private house every year. You park on the road and turn your radio on to a specific channel. It's at 1585 East Second St., Pass Christian. A nice drive down Beach Blvd. heading west about 25 minutes. When you see Super Walmart, make a right just before it. Go about two blocks to Second St. turn left and the show is about 3 minutes down on the right. It goes 7 days a week from 5 to 11 p.m. Show lasts about 30 minutes.