Osaka/Kyoto or Tokyo first?

Going for a Japan visit in late December (leaving Boston on December 20th and returning January 2nd). This will be my first time visiting the country. I'll be coming from Boston (which has a nonstop flight to Narita). Primary focus for the trip is good eating second is Japanese culture (anime in particular). I only have time for a short trip and have a job that pays relatively well, so maximizing my time is my primary concern (for example, buying a JR Pass that excludes Nozomi would for me not be worth it).

Do the pros and cons in being in one location (Kyoto/Osaka or Toyko) on December 31st/January 1st, make one generally a better idea than the other?

I'm assuming time saving wise it is best to grab a flight either from Narita to KIX at the beginning of the trip, or from KIX to Narita at the end of the trip, versus taking the shinkansen both ways. Is that correct?

Thanks in advance for any advice you can give. And apologies for asking about what may seem to some like minutiae, I'm just so exited for the trip.

JR Tokyo station to JR Shin-osaka station on Shinkansen takes only around 3 hours. If you find a good connection from Narita to KIX upon arrival, or KIX to Narita before departure, that is good, but otherwise, you can simply buy individual Shinkansen tickets (even both ways). Unless you have a good connection, for example if you had to arrive in Narita, then travel to Haneda (another airport in central Tokyo) by rail, and then fly to KIX, it would not make much sense.

If you are flying out of Narita on Jan. 2nd, I'd say it would be better to be closer to Tokyo by the 1st, isn't it? (Unless your flight is far late in the day.)

If you want to start or end your trip in Kansai, flying into the country through Narita/Haneda and leaving through Kansai International will probably save more time, if you can do so at a reasonable price.

I don't see why a JR pass is not a good option for you. As long as a JR pass for your itinary is less than the cost of individual tickets, it is generally a good option. A Hikari train only takes 25 minutes longer to get to Shin-Osaka station than a Nozomi train, and they have better access to the city centre compared to Airports. I don't know exactly how much time you need for check-ins and security checks for Japanese domestic flights, but I expext they will take more time compared to boarding a Shinkansen, which is not much more complicated than boarding a local train.

You mentioned 'anime', thus Akihabara in Tokyo is a MUST SEE!!!

Otherwise, Kyoto will be culturally more significant with the temples and all, Tokyo more of a metropolitan for those that want a broad taste of city life.

Both have delicious food choices, can't go wrong with either.