How are your flights scheduled?
Which airport(s) will you fly into and fly out from?
In 2018, the Golden Week will last until the 6th of May:
the weekend from Saturday, the 28th of April will be expanded to be until Monday (holiday), the 30th;
the 1st and the 2nd of May will be weekdays;
the 3rd to 5th of May, which are consecutive holidays, will be followed by Sunday, the 6th.
The 7th to 11th of May 2018 will be normal weekdays. https://www.japan-guide.com/e/e2282.html
I recommend that you, after getting through the immigration procedure, as soon as possible, will visit a JR ticket counter and try to reserve your Shinkansen train seats.
Also a domestic flight from Tokyo Haneda [HND] to Osaka Itami [HND] may be your option if you successfully book it in advance.
- ANA Experience JAPAN Fare https://www.ana.co.jp/en/us/promotions/share/experience_jp/
- How to travel between Itami Airport and Kyoto https://www.japan-guide.com/e/e2433.html?aFROM=2158_2433
(A) You will fly out from Kansai [KIX].
In this case, it would be better to head to Kyoto Station on 4 May or, in the morning on 5 May at latest.
From the afternoon on 5 May to the night on 6 May,
westbound trains on the Tokaido Shinkansen may get relatively crowded with passengers returning to western Japan.
Getting to Kyoto on 7 May may not leave you time enough for trips in Kansai Region.
(B) You will go back to Tokyo and fly out from Narita [NRT] or Tokyo Haneda [HND].
In this case, you can avoid the expected peaks of the crowdedness in Shinkansen trains,
by heading to Kyoto Station on 2 May and back to Shinagawa or Tokyo Station on 7 May.