11 Days in September

We are wanting to go to Japan 11 days in September 2009. As we will only be there for such a short time we are thinking about spending the following itenary:
6 days Tokyo
5 days Kyoto

From here we are wanting to do spend time in the actual cities and then day trips to places like: Kamakura, Mount Fuji/Hakone, Hemeji Castle, Osaka, places like that.
Too short of a time but what can you do....

Anyway, would something like this work? (this way we have two different hotels)
Would we need a JR rail pass for three of us or would it be cheaper to do something else?
From a day trip where would be the furthest you would go for a day?

Anyway, would something like this work?

Yes, that is a very standard and recommended thing to do.

Would we need a JR rail pass for three of us or would it be cheaper to do something else?

The cheapest would be travel by overnight bus. A 7-day Japan Rail Pass comes cheaper than regular train tickets if you make a round trip between Tokyo and Kyoto, but will not pay off if you travel only once between the two cities, i.e. you enter Japan though Tokyo and leave through Osaka (or the other way around).

From a day trip where would be the furthest you would go for a day?

Your selection of day trips sounds good and all can easily be done. If I would consider an additional one, it would be Hiroshima from Kyoto, which is consdierably farther away than the other destinations, and might change the rail pass situation.

FYI
http://www.japan-guide.com/e/e2400_tokyo_9.html