Shinkansen Kyoto to Tokyo on Dec 31

Hello all, my wife and I are headed to Japan on a last-minute trip due to a great fare we found, it's the first time for both of us and all the information seems a bit overwhelming. We are in Kyoto from Dec 27-31 (Kyoto 2 days, day trips to Osaka and Nara), then the plan was to Shinkansen from Kyoto to Tokyo on Dec 31 for the remainder of our trip (we'd be in Tokyo for a week, hoping to make daytrips to Nikko and elsewhere).

My question:

We aren't doing JR Rail Pass since we aren't really train traveling too much to justify it. But I just wanted to ask you all if it would be no problem to buy a Shinkansen ticket from Kyoto to Tokyo on Dec 31 (is this a busier day than normal?). Should I pre-purchase tix at the Kyoto station when we arrive for the 31st, or should I be able to buy on day of travel?

Second question (if have any good suggestions):

Where are the best places to spend NYE in Tokyo? It's our first time in Tokyo and we'd love to experience it on NYE, but at the same time we don't want to do something like Times Square in NYC where we'd have to queue for hours and it'd be a huge security hassle, etc?

Thanks to everyone :)

NYE is a time for family in Japan, and many people will be travelling on the 31st. Definitely book tickets as soon as you arrive in Japan, and have several options available in case your first choice is booked out. If all trains are sold out, you'll have to line up for the unreserved carriages (and possibly stand if it's really busy).

As NYE is a family affair, parties and countdowns aren't the norm in Japan. Consider visiting a temple or shrine to see in the New Year in unique Japanese style.

Kyoto to Tokyo on Dec 31 no problem. There are too many trains to check them all, but I haven't found a single one that's booked out.