Kalymnos as a lens?

Hello all. So I was planning on doing some extensive traveling after uni, but unfortunately my budget has been hacked to death so I'm in the process of trying to find the most "full value" spot possible. I was thinking of flying to London->Athens->Kos(I'm from the US) in April and ferry on over to Kalymnos for several months and then retrace those steps in June. Conceptually its cheap, and I can always ferry over to Bodrum if I want to check out somewhere else. And since I'll be there for a decent amount of time, I naively fantasize about making friends with locals, using Kalymnos as a lens to better understand Greek culture, etc. I guess I'm just hoping you all can share some of your thoughts. Is this the cheapest way to get there? Will the routes keep me plenty entertained? Any advice on apartments? Does Bodrum live up to the hype? Most importantly, how nice are the locals and are they interested in making friends with the tourists? Thank you all!