Japan in New Year

Hi all! Need some advise pls. My family and I will be traveling to Japan for the New Year. Unfortunately, we weren't able to check ahead and only found out recently that some establishments will be closed during this season. Our tentative IT as follows:
Dec 29: Arrival at Narita at 13:10hrs, then proceed to Osaka
Dec 30: Osaka (Aquarium, Sky bldg etc)
Dec 31: Day trip to Kyoto
Jan 1: USJ
Jan 2: Osaka tour (Osaka Castle etc...)
Jan 3: Day trip to Hiroshima
Jan 4: Osaka to Tokyo
Jan 5: Depart from Narita 13:55hrs and back to home
I considered this sked i found online for the IT above:
*Osaka Castle closed from Dec 28 to Jan 01
*KYOTO: Imperial palace and Nijo Castle close from Dec 26 to Jan 04
*HIROSHIMA: A-BOMB museum close dec 31 & 31

I would like to seek advise on what to do and where to go in Kyoto on Dec 31 pls. Also, would it be a bad idea to be in USJ on Jan1? Meaning more crowded? Or less crowded because of the holiday? Any advise to improve this IT would be highly highly appreciated.
Thank you!

This is the crowd calendar for USJ: http://www15.plala.or.jp/gcap/usj/

It estimates crowds at around 30,000 people just to the border between yellow and orange. I've never been on a day that crowded, but I just did Disney Sea on a day that was supposed to be Orange and it was a pretty miserable experience. Everything had 1 hour plus lines including many food kiosks and there were no FPs left by the time I got there because I had a Twilight Pass.

If you want to go to USJ be there 20 -30 minutes before opening and consider buying one of the express pass tickets ahead of time. The first 1 hour is a theme park is generally the shortest lines.

For Kyoto, I would see what you are interested in seeing and check out the hours that day.

Good luck

on Dec. 29, if you go to Osaka from Narita by trains, those should be very crowded.
on Jan. 4, also I expect that it is very crowded.