As I recall, national holidays are days off work for schools, banks, most offices. But everything else works as usual, transport, shops, everything at the airport. The Japanese don't tend to take off the whole week, they just take off the national holiday though these days they sometimes tack it on to a weekend.
Respect for the Aged day used to be 15th Sept so maybe I'm way out of date here. The autumn equinox is still 23rd though.
From what I can see of your plans, no need to change anything though transport will probably be more crowded with the national holiday. You may want to book your shinkansen tickets ahead of time.

Thanks. (Three different sites all have Sep 20th.) If I'm using a JR pass, can I book the shinkansen from the US, or do I have to wait until I convert the voucher in Japan? Although I may pay for the Tokyo-Kyoto train separately anyway since I'll buy a 14 day pass for a 20 day trip. Crowds are what I was wondering about - I was going to do Hakone on a Wednesday in the hope it would be less crowded.

Don't know about booking from the US, I've only ever done it when I'm there after I've converted the JR pass. It shouldn't be hard to get a single seat. I'm sure Hakone will be less crowded on a Wednesday.

There will be three days off Sept 21,22 & 23 this year for those two holidays and there might be some heavy travel as some families visit graves of their ancestors. Select September to see the schedule:

http://www.japan-guide.com/event/

Most main venues in Hakone will be open.

Airport banks will be closed but the money exchanges are open 365 days. They close after 18:00 or 19:00 though. I used the airport ATM only once during our first visit and remember something strange about the last thing you have to do before you get your money out so I never used again at the airport. Had to keep taking my card out and doing it over and over so now I just get whatever I need from the currency exchangers to tide me over. The rates exchanges at the airport are here:

http://www.narita-airport.or.jp/exchange_e/index.html

Tsukiji Fish Market would be closed on 9/21 for the holiday btw

Aloha!

Just as a matter of interest, it looks like Japanese national holidays have been 'rationalised' since my day. They used to be on specific dates come what may. Looks like now they are 3rd Monday in September and other such sensible dates. Progress!

"there might be some heavy travel" - unfortunately, pushing this trip out a week messes up some things later on. I guess I'll just have to cope with the crowds - but it does sound like I should try to book the Tokyo-Kyoto train ahead? And would it be better to visit Nikko or Kamakura on Sep 22 and Hakone on Saturday Oct 9th?

"Tsukiji Fish Market would be closed on 9/21 for the holiday btw" - well, that's what I expected, but this site - http://www.tsukiji-market.or.jp/etc/calendar/2010.html - seems to say otherwise?

Thanks.

You can only book train reservations in advance from the US on the JR East routes. Nothing south of Tokyo. http://www.jreast.co.jp/e/eastpass/index.html
I know the JR website had a virus attack in February and a lot of their online services have not been restored yet.
There are a bunch of train passes available besides the 7,14 and 21 day versions but would have to see proposed itinerary to see which would be best

You might bump into another national holiday around Oct 9th: Sports Day used to be 10 Oct but now it says it's the second Monday in Oct which would make Oct 9 part of a long weekend...
It looks like dodging the crowds will be tricky!

I know you don't like crowds but there is a matsuri in Takayama Oct 9-10
http://www.jnto.go.jp/eng/indepth/history/traditionalevents/a54_fes_takayama.html

As far as train reservations go, you should be alright with making them when you convert your voucher. The Tokyo-Kyoto route has more trains per hour than any other route and a single traveler would have no problem except maybe during rush hour.