There are many islands around Cartagena that you can visit in one day called Islas del Rosario. Below you will find a quick description of the ones I have been, and the ones I recommend depending on what you are looking for:
1) Playa Blanca in Baru: This is the most popular one. White sand beach and light blue warm water. However, due to its popularity, the beach is extremely busy and full sellers which may be a bit annoying. You can find tours in Cartagena´s main harbor from 15 dollars. This includes the speed boat and lunch (fish, plantain and coconut rice). Cocktails on the island are around 7 dollars.
2 ) Tierra Bomba: This is the main island in front of Cartagena. The beach is not as nice, but it is close and convenient ( just 10 minutes from Cartagena) and is not as crowded. Here I have been in 2 hotels:
a ) Blue Apple Beach: I liked this one: it is small with allocated sunbeds, it has a pool next to the beach with DJ, the beach is nice and feels almost private, the water is warm, and the food, cocktails, and service is amazing. If you are looking for something a bit more private, with good service and a nice atmosphere, this is the place to go. You can book directly with them at https://www.blueapplebeach.com/ or with Booking.com. It cost 75 dollars per person and includes the speed boat, the allocated sunbeds and lunch.
b) Tropical in: This hotel is located in a different part of the island. The beach is a bit nicer than the one on Blue Apple Beach, but the hotel is not as nice. I think it is a bit overpriced for what they offer. Between both I would stay in Blue Apple Beach considering that the price is pretty much the same.
3) Bendita beach: This island is beautiful, the sand is white and the ocean is light blue and warm, it feels like a paradise. However, the island does not have good infrastructure, and therefore, there are no pools or bars on the island. Thus, if you are happy to sit by the beach, relax with your drinks and just enjoy nature, this is the place to go. If you are the type of person who likes good service and fancy having a nice bar and pool, I would not recommend it.
4) Cholon: If you are looking for a party, this is the place to go. You will find many people partying in boats with loud music and drinks. The water is amazing, but with so many people drinking and partying on it, it may not be as clean.