The Hard Rock Hotel is on the hotel strip in Cancun. A shopping mall for souvenirs or other items is down the road. You can walk there, but it is farther, so if interested you can take the bus down and back for a couple of pesos.
Hard Rock Hotel has multiple excursions you can go on through the hotel. Most are day long tours, so be prepared to wake up early and be away from the pool for the day. These include visiting a cenote, swimming with dolphins, or visiting the Mayan ruins of Chichen Itza or Tulum. You can set these up with the hotel when you arrive, just make sure it's not scheduled for the 26th.
There are multiple things that go on right at the resort. This includes activities by the pool including exercises in the water, trivia, contests, dance parties, and pool games. At night, you can enjoy a free show. There are also events you can sign up for including wine or tequila tasting. There is always something going on, so if you don't want to leave the resort you don't have to!