JR Pass or not?

With your itinerary you'd come up a little short. But you can easily make up the difference by some good side trips - in the Tokyo area, you could take a day trip to Nikko, which is well worth it. Near Kyoto, Nara is a must see place for at least half a day, and Himeji Castle is Japan's finest and will have it's multi-year renovation finished in just a few weeks.

Thank you for the response, Toraneko! Would it be very short, or about the same? If it's only 10-20 dollars different or so, I think it would be worth it for the flexibility.

If I recall, ballpark was a bit over 3000 yen. There is some convenience in not constantly having to go buy tickets, but only you can decide if it's worth the price differential. I'd suggest you take one of the side trips to make the Pass worthwhile anyway, in which case it's all a moot point.