Kyoto is the former capital of Japan.  The city was also founded over 1000 years.  As a result there is a lot of traditions and history.
Getting to Kyoto-
The city does not have an airport of its own.  There are two nearby airports, Kansai International Airport (KIX) and Osaka International Airport (ITM).  Flights to and from the USA are infrequent from either of these two airports, so you will most likely need to arrive in Tokyo at either Haneda (HND) or Narita (NRT) and transfer by air or by Bullet Train (Shinkansen).  The Bullet Train from Tokyo to Kyoto is about 2.5 hours.
Kyoto is a fairly large city.  When looking for a place to stay, the internet is your best friend.  Most major international chains have one or more well located hotels in the city.
Now that you are in Kyoto, what is there to do?
Kyoto Hanatouro Festival