@mrwunrfl - ah, that makes perfect sense!

If the difference in prices for open jaw is about equal to the cost of the JR pass, think about the opportunities you will have with the pass (and the costs you would avoid by having it) and the savings in time by not having to backtrack...

For a splurge dinner, I still savor my memories of a full-out splurge for French kaiseki at Misoguigawa in Kyoto. Advance reservations are a must.
http://www.misogui.jp/original13.html

New Years in Japan:
http://www.japan-guide.com/e/e2276.html
Seriously, use that search box! :-)

I always get at least one burger when in Japan, but from Japanese chains - my two favourites are MOS burger and Freshness. MOS in particular has a Japanese take with more sauce and a different flavour to the meat patties. Love them! As for small, well, Japanese generally don't eat or serve huge portions - suited us very well as I prefer to eat small and more often so I can try more delicious local food!

For (relatively) inexpensive sushi in Tokyo, look at Zanmai. We've visited various branches of this chain over our 3 trips and never been disappointed. Huge menu too and very fresh fish.

Katsu is popular and there are many fast-food style chains, including a bunch of curry katsu places. (Katsu is the breaded fried pork, usually served with cabbage, but the curry places usually serve with rice and curry sauce).

Ramen places are often cheap.

Gyudon (beef bowl) places, there are at least two or three chains that sell this, we have eaten at them when looking for a quick, cheap and tasty meal.

Of course, buying a meal from the nearest konbini (convenience store) is also really enjoyable - good for budget sandwiches, sushi sets, and all sorts. Incidentally, mainline train stations always have budget food options, including some amazing bento box meals that we love. Known as ekiben (eki = station, ben is short for bento).

You can visit the Imperial Palace in Tokyo on Jan 2:
http://www.japan-guide.com/e/e3017.html