I read, go to the spa, chat with people I meet, doze, listen to music (on headphones!) and (and it is very bad of me!) think about longer term work projects! Many hotels also have wifi that works on the beach / around the pool. You could download some TV shows etc. to watch as well.

Most beach resorts have activities during the day, say, poker tournaments, cocktail making classes, trivia, wine tastings, language lessons etc.

I broke my knee badly some years ago, so from my 'lessons learned', you might find hanging around the pool easier than the beach (the sand can be a PITA to walk on with a broken limb because it moves under you), you may want to ask the hotel for an accessible room (ground floor - many of the hotels don't have elevators) with a seat in the shower, close to the pool area (some of the resorts are pretty big). On the plane you might want to book an upgrade. If you don't, please please tell the person in front of you about your busted knee, and ask them to let you know before they recline (you do not want the seat hitting your knee!) I booked bulkhead when I flew with a duff knee, and then after take off rested my leg on my carry on bag. The ability to do that will depend on the aircraft tho.

If you do boating, you should go to a marina to get on and off (many of them board from either in the water, or a little shuttle boat out to the larger boat, both of which would be very hard to get in to with a bust knee (big step, full weight on one leg, moving surface).)

Also watch out for wet floors. It can get rainy in Punta Cana, and a lot of the hotel floors are polished marble, which gets pretty lethal when wet. Pack shoes with very good grip, and maybe order room service if it gets really wet!

Oh one more thing, you will likely have to come down steps (no air bridge) at Punta Cana airport, so if you will have trouble, let the airline know in advance.