The train vs plane debate for travel between Tokyo and Kyoto is a long standing one. Most people on this forum recommend the train (shinkansen - bullet) but there is a strong case for flying too.

Here are some sample threads where it has been discussed at length:
http://flyertalk.com/forum/showthread.php?t=527891
http://flyertalk.com/forum/showthread.php?t=464795
http://flyertalk.com/forum/showthread.php?t=609783 (this one's a monster)
but there are many more.

I'm concerned about you both spending such a short time in Kyoto. One day is barely enough to scratch the surface of this city, even three days would be a short trip.

Economic option
You can get return shinkansen travel to Kyoto from Tokyo with accomodation included at both these websites:
http://www.jtbgmt.com/sunrisetour/
http://www.iace.co.jp/english/fare/pkg/kyoto2007.htm
from 19,500yen for one night and two days in Kyoto
The return rail fare without a JRrail pass would be about 26,000 yen, so it's a considerable saving.
This is for travel on the Hikari bullet train.

The fastest bullet trains are called Nozomi - you can still do the excursion using these trains if you prefer:
http://www.jtbgmt.com/sunrisetour/

Another option, of course, would be to arrive in Japan at NRT(Tokyo) and leave from KIX(near Kyoto)... or vice versa.