Japan Rail Pass or not?

Bides

We are travelling to Osaka for 8 days in August. We need to be able to get around locally to follow our child while they play sport at different venues (won't know venues till we arrive)and I would also like to make two trips to Tokyo (Disneyland) during our stay. What would you suggest is the best/most economical? There will be one adult and 9 year old child. Thank you.

Tenjin

A Osaka-Tokyo round trip almost pays for a 7 day JR Rail Pass, so that plus a small side trip would do it. If you want to do 2 full round trips in a week, that would make the pass pay off and then some, but it would not be time efficient at all - one way would be about 3 hours to Tokyo Station, and more to get to Disneyland, so an overnight in Tokyo would make far more sense.
Locally within Osaka you could also use the pass for the Osaka Loop line, but there is not much in terms of accumulating savings in it.
Plus you did not mention seeing Kyoto and Nara, which are the crown jewels of traditional Japanese culture and well worth a lot of your attention.