I am going to assume you guys are talking dollars, seeing the aforementioned figures completly exceed what I have spent there for 2 weeks in Euro's
No matter.
Coincidentally, I will be in Japan at the exact same dates that you will be
As far as Kyoto goes, despite the distance between it and Tokyo it is still possible to do it as a day-trip.
You'll need to ride the JR Tokaido Shinkansen line and have the choice of either the Nozomi version of the train (slightly more luxorious) which gets you there in 2 hours and 20 minutes flat, or the Hikari version (slightly less luxorious) and takes roughly 20 minutes longer than the Nozomi.
Alternativly the cheapest train option is the kodama tough it takes a whopping five hours to get there, times 2 your looking at 10 hours of sitting time: I.E not a daytrip.
The Nozomi and Hikari cost alot of money and tickets need to be reserved beforehand. Last time I checked a month or two ago that was about 180 euro's on the Nozomi for a single trip (i.e times 2 to get back) However, if you have the Japan rail pass than you can get a big discount on these high-speed lines - they are absolutly not for free even with the JR rail pass tough, but the JR rail pass is worth it if you go beyond Tokyo/Yokohama
See the official JR railways website for timetables, fares and information on getting about.
JAPAN RAILWAYS GROUP - Home
Consider doing the following (as I am doing the same)
Go from Tokyo directly to Osaka and pick a hotel there.
Reason ? It can take as little as 30 minutes to go from Osaka to Kyoto.
Since your goal is to both taste the nightlife and historical part of Japan means that you can
enjoy the nightlife in Osaka in the nighttime, but during the daytime visit gardens,castles and shrines in Kyoto. You could't do it effectivly vice-versa.