There are a number of interesting islands in the vicinity of Kos which you should definitely consider visiting. Kastri for one is a must see as it is situated in the Kefalos bay and is one of the most picturesque sites on the island. You can swim over quite easily and visit the church or just rent a pédalo and just pedal over.
Islands to the South of Kos
On the Southern side of the island the most popular day trip is the one to Nisyros out of Kardamena. You get to visit the volcano and to spend the afternoon in Mandraki a village that has maintained a more traditional feel. For the more adventurous amongst you there are quite a few places to visit including Emporios, Nikia and Paloi but you will need to rent a scooter or a car to get there. There are also trips to Gyali out of Nisyros if you fancy something different but that might be a bit of a complicated endeavor and in any case you might need to spend at least a night in Nisyros to make it worth it. There is also the option of going to Tilos out of Kos Town but you will definitely need a few days to actually get to see the island. Have a look at an Octopus in my ouzo an interesting blog with some insights on the island of Tilos.
Islands to the North of Kos
Towards the North there is a plethora of islands in the vicinity of Kos. Kalymnos is very close to Mastichari (20 minutes by fast boat and 50 minutes with the ferry that has the added advantage of transporting cars) and there are frequent connections throughout the day. Kalymnos is a big island but it is rather rugged. It is a climber’s paradise and climbers tend to visit all year round. The landscape is quite beautiful although rugged but there are also a number of very nice coves where you can take a dip in the clear turquoise waters. There are plenty of things to see including a number of villages: Myrties, Vlihadia, Vathy, Emporio just to name a few and you would probably need a few days to cover the whole island if you put your mind to it. Kalymnians are seafarers and are renowned for their sponges (hence their presence in countries where they used to dive for sponges including the US-Tarpon Springs,Gary, IN, and Campbell, OH- and Australia – Darwin and Melbourne) and their seafood. So don’t forget to grab a bite to eat if you are into seafood in general. On the western side of Kalymnos lies Nera which is a relatively large island on which there is just a church. It is mostly populated by seagulls and can only be reached during the summer via trips out of Kos. On the other hand, there is the easy option of Telendos which is very close to the Kalymnos mainland and has regular connections (every half hour) out of the village of Myrties. On Telendos you can spend the day swimming and eating at the tavernas, go and visit the monuments that abound or even explore the caves in the mountainous areas.
East of Kalymnos there are a couple of Islands in the vicinity of Kos. The island of Platy can be reached via the three island tour out of Mastichari or Kos Town that includes the islands of Kalymnos, Platy and Pserimos. It is a very small rocky island and there is not much to do. A few years ago a house was built and a family moved there in an effort to populate the island. The island of Pserimos can be reached from Kalymnos throughout most of the year and from Mastichari during the summer on a daily basis (you can actually spend the day there). It is a relatively big island with a small population. There are a number of beaches and places you can visit (Marathonda, Vathi, Grafiotiosa) if you want but most people prefer to remain in the village next to the harbor and just swim and grab some lunch in a very laid back atmosphere.
Beyond these relatively easily accessible options there are a number of other islands you can visit and we have included some of them in this website. Lipsoi and Leros are easily reachable on a daily basis while Levitha and Kandeleousa are somewhat more difficult to reach as you would need to hire a boat to get there.