Yep - What he said.

Train - no question
 

In case anyone misses the trend, the answer is train, train train. I lived in Tokyo 5 years and went to Osaka at least monthly and in all that time I may have taken the plane once. Getting to Haneda is a hassle from the city and the planes can be crowded (and expensive). There are several different Shinkansen trains and if you are into the small details try to get on one of the newer ones. They have different names (Nozomi, Hikari, etc) and I don't remember what the name of the fastest one is (I think it is the 700 series). On the way to Kyoto sit on the right side just in case Fuji-san is visible. Rare, but why take the chance of missing that spectacular sight. I do recommend spending the extra for the Green Car (first class) and unless you like smoke be sure to get non-smoking. Generally the obento boxes on the train are good, or there are tons of good obento shops in Tokyo station to get something before you board the train.

When in Kyoto you might try staying at the Three Sisters Inn (Okazaki, Sakyo-ku, Kyoto 606-8321. Phone (075) 761-6336 (reservations 8 am to 11 pm); international 81-75 761-6336). It is a western friendly traditional style inn.

One of the best holidays of our life was the 3 days we spent in Kyoto at the end of our 5 year stint in Japan. Kyoto is a very warm and magical city.
Gambatte kudasai (good luck).

Though I hate to bring up the topic of green vs ordinary, it has always been my opinion that unless you have some extra change to throw around, Ordinary cars have always been perfectly fine.

I wouldnt even consider flying to get from Tokyo to Kyoto. If you can try for a seat of the right side of the train at a window going to Kyoto. Left coming back. Hope it is a clear day ;)

Further to the other posters, I'd also like to add that - if you get the JR Pass - it's also valid on the Narita Express, which you might well be expecting to take from the airport in any case.

More savings.

Yes its useful for the Narita Express coming from the airport, however if you use it coming FROM the airport to tokyo, then spending a few days in Tokyo, make sure your trip to Kyoto and back falls within the 7day validity of the pass to make it cost effective.

Ex.
Day
1 Activate JR Pass, NRT-Tokyo
2 *
3 *
4 *
5 *
6 *
7 Leave Kyoto back to Tokyo (+Tokyo back to NRT)

If not using the railpass from NRT-Tokyo, activate the JR Pass for the day you plan to leave for Kyoto and that your return is within 7 days, then you can use the Narita Express on the Return trip to NRT from Tokyo.

You've gotten lots of responses, most of which I agree with. but there are a couple of suggestions that haven't been made yet.

You mentioned cabs in your original post. DO NOT even consider cabs for airport transportation. A cab from NRT into Tokyo will run almost $300.00 and one from KIX to Kyoto would be over $200.00. Even from Itami to Kyoto would be a big hit on the wallet. Trains and limo buses are the way to go in Japan. I prefer trains, but the buses have their supporters.

If you are planning to spend time in Tokyo, then go to Kyoto before going home, you might consider checking to see if you can do an open jaw flight arriving in Japan at NRT and leaving via KIX. That would save the return trip to Tokyo. I've done this and liked the flexibility. I don't know if NWA flies into/out of KIX, but it might be worth looking into.

JR

In my two trips on the shinkansen, I've also found the ordinary car to be fine. As for the taxi issue, I agree that you should find a bus or something. There are a lot of buses that run from NRT-Tokyo and from KIX into Osaka for about $30 or less.