Two nights/three days

I am wondering if I base myself in Kyoto for two nights/three days and having day trips to Osaka and Hiroshima using the train. Or would it be better to change accomodation?
I have a very small time frame so I have to use it effectively.
Is Osaka worth going to if we will have already spent two days in Tokyo?

Depends on the rest of your itinerary, i.e. what you do before and after Hiroshima/Osaka. But a day trip from Kyoto to Hiroshima is, indeed, possible.

There is so much to see in Kyoto: a day trip to Osaka really isn't worth it in my opinion: BUT on the other hand you can base yourself in Osaka, and do day trips to Kyoto and Hiroshima: that way you are a little closer to Hiroshima, and have the advantage of the night life in Osaka....

I agree with fmj that there is so much to see in Kyoto that you don't have to spend a day in Osaka :) For staying over, I prefer Kyoto (that's a place where you "soak in" the atmosphere) as against cluttered Osaka, though.