If you make the roundtrip between Tokyo - Osaka/Kyoto within a 7-day period, then the 7 Day Japan Rail Pass makes sense. If you are going only one way from Tokyo to Kyoto/Osaka and flying out of Kansai airport, then, no. Buying individual train tickets would come out less expensive. To go to Hakone, you can take Shinkansen to Odawara, then from there buy Hakone Free Pass (within Hakone, all transport including cable cars are non-JR) to travel within Hakone.
OR, if you decide not to buy a JR Pass, then buying a version of Hakone Free Pass that includes the train ride from Shinjuku (Tokyo) might make sense, though with this ticket you will be returning to Tokyo.
For a 10-day trip, unless you have particular interest in Nagoya, I'd say, no.