Naoshima island or takayama

which one do you prefer

When?

from where? (last area or stay)

i will travel from tokyo to takayama
or i will skip takayama and go directly to kyoto and osaka and will do a daytrip from osaka to naoshima

or i will stay at Okayama
and do daytrips to naoshima, hiroshima and Miyajima

The two are completely different, so it really depends on what kind of experience you are looking for.

I've not been to Takayama, but I know it's famous for it's traditional buildings and atmosphere (and festival).

Naoshima is a modern art island. It's a really nice daytrip (better from Okayama, I think, so you can start early but doable from Osaka). The art islands are really unique, so if you like art and are looking for something that is Japanese but different from the usual sites, Naoshima is great.

We've not been to Naoshima, but love Takayama and have been a few times. The trip through the mountains is great, the beef is brilliant, and the town is very nice. Most people only stay a day or so but we are happy to relax there for a lot longer.

I've been to both and I prefer Takayama because of the small castle and the great garden.

However, if you are interested in art, then you should check out Naoshima.
Here's a detailed post with lots of photos, so you get an idea of it: http://zoomingjapan.com/travel/naoshima-art-island/