Should we buy a JR pass for 7 days?

Hi!
We have a 6 day Japan trip coming soon. We will arrive in Nagoya and will stay for 2 days then 4 days in Osaka with day trips to Kyoto.

Would the JR pass be the best train pass to buy?

I haven't checked, but don't think a JR pass is likely to pay off with that (when I visited, Tokyo to Kyoto and back again was basically the distance where a pass equalled the cost of individual tickets, and it doesn't seem like you'll be doing anywhere near as much travelling).

The seven day JR Pass is overkill. Look into purchasing a 5 day Kintetsu wide area pass.

http://www.japan-guide.com/e/e2357_006.html

This will provide the following:

Airport transfer from the Airport to Nagoya.
A five day pass on the Kintetsu Pirvate rail system.
Airport transfer to Osaka Airport from Namba(Nankai) Station.
Three reserved seat reservations, during the five day period, on the Kintetsu line. You will use one of these t go from KintetsuNagoya Station to Osaka-Namba Station, and your will probably use the other two to go from Osaka-Namba Station to Kyoto Station and back.

You will probably need an IC card, that will be usable in Nagoya, Kyoto, and Osaka, for travel outside of the Kintetsu Pass coverage.

http://www.japan-guide.com/e/e2359_003.html

The IC card will cover trips, such as If you wanted to a day trip to Universal Studios in Osaka, for instance. If you are planning a day with lots of hops between different places, such as the Temples and Shrines around Kyoto, you may want to look into a day pass.
This will be a lot less expensive than a 7 day JR Pass.

I hope this helps.

Thanks so much for the help!

Just in case you intention was to ride Tokaido Shinkansen between Nagoya and Shinosaka, there is a special discount ticket to travel on the Kodama (the slowest ones) trains for just 4300 yen.

http://www.jrtours.co.jp/kodama/en/