We recently returned from a brilliant trip to Kalymnos. Being a couple composed of a vegetarian and a vegan, we wanted to help anyone else who is thinking of coming here and happens to be on a similar diet.
Firstly: It is much easier to stay in a studio with a kitchenette, where you can make some of your own meals. This is probably a very obvious thing to state, but keep it in mind as some of the hotels will only have a fridge in the rooms. We managed in a hotel, but brought some food from home to help vary our meals.
Secondly: Soya milk can be obtained in Kalymnos! We found it in one of the smaller supermarkets in Massouri and in two of the larger supermarkets on the road from Massouri to Pothia.
Places to eat out: We found Glaros Snack Bar in Massouri to be excellent. There are lots of vegetarian snacks that can also be made for vegans and gluten-free diets, such as chickpea burgers, chilli bean burgers, falafel and dolmades. One of the owners is vegetarian herself and understands the need for a variety of tasty food! They also make sandwiches which you can take away to the crag for lunch, amongst many other things.
Noufaro restaurant, also in Massouri, was great too. The menu has helpful smiley faces next to the vegetarian dishes (although some of the fish dishes also have these, so check before ordering.) We found the houmous to be simply amazing. They also have a daily vegetarian special which is often vegan, for example green beans in a tomato sauce. Their desserts are great too!
Harry's Paradise Restaurant on the other side of the island, Emborios, also has a selection of vegetarian food which is often home-grown as well as being home-made. Their selection is best for veggies, slightly more limited for vegans.
There are other restaurants and snack bars on the island which offer standard climber or traditional Greek food which can be vegetarian (omelettes, crepes, stuffed vegetables, salads and so on) so go explore!
We could not buy any tofu, cheese substitutes or soya slices locally (as of June 2012) so you may wish to bring these to the island if you can't live without them. Don't bother bringing dairy-free margarine as the local olive oil is much nicer on your bread!
We hope this has been useful!