I've been to Japan three times now, all of them solo trips for 3 weeks or so each. it's a great country to visit and can be lots of fun. is this your first time going to Japan? are you getting the Japan Railway Pass? how long would this trip be? if you don't mind sharing your plan so far, I can definitely add on some more suggestions to it. keep in mind that, other than the closures around New Year that I mentioned, the temperature can also be a little tricky. anywhere outdoor is really cold during that season of the year, but as soon as you step into any place in-door like a store, restaurant, even on the train, it's sweat inducingly warm. one can catch a cold or something very easily because of that, so make sure to dress in layers and wear things that's easy to put on and remove.
for Hokkaido, where are you going? I'm going to guess mostly Sapporo and Hakodate? maybe Otaru? if you can, try Hell Valley area in Noborietsu. it's an onsen town with plenty of hotels which all has their own hot spring baths. if you're not driving in Hokkaido thou, keep in mind trains and buses can have longer wait time than the mainland. I'm planning my own trip right now for next year and part of it would be driving across Hokkaido for a week or so.
the Robot Restaurant show in Tokyo is sadly closed now due to Covid, along with a lot of other cool stuff in the city, so make sure to check for the most updated info on the places you plan on visiting. I'm a big fan of Asakusa, and Shinjuku. can find lots of good eats at these two areas. the Ghibli Museum is great too of course, but it requires advance booking and it's kinda out of the main Tokyo area, so make sure to plan accordingly. if you want a good view of the city from up high and don't want to pay for the fee to go up Tokyo Tower or Skytree, consider Tokyo Metropolitan Government Building. the twin tower building has two observation decks up top that provides a bird's eye view of the whole Tokyo area. and it's completely free. it also has an government employee cafeteria that's open to the public. the food is actually pretty good there too if you want to grab a quick lunch.
when you said you'll be going to Osaka too, do you mean just Osaka or Kansai in general? if you have time, I would at least recommend going to Himeji, Kobe and Nara also. you can probably put a day to go to Nara in the morning and then return to walk around Osaka in the afternoon/night time. you can also fit Himeji and Kobe both in one day. head to Himeji in the morning and then visit Kobe in the afternoon, plus have dinner there. since you're going with your girlfriend, might I suggest you also check out one of three greatest night view in Japan from up top the observatory on Mount Rokko? it's a pretty romantic and beautiful view. just FYI, the other two night views are in Nagasaki and Hakodate, the later of which I imagine you might visit too when you're in Hokkaido.
do you plan on going to Kyoto at all? because Kyoto would probably need 3 to 4 days too. there are so many great places to see in that area. most well known being the golden pavilion in Kinkaku-ji, and the Senbon Torii pathways in the Fushimi Inari Shrine. there are also some really awesome places to see if you go to Arashiyama in the west side of Kyoto. Otagi Nebutsu-ji and Adashino Nebutsu-ji being two of my favorites. the Toei Kyoto Studio Park over in the Uzumasa area can be pretty fun too, if you're into the Japanese period films and stuff. not to mention many of the other Kyoto must sees, like Kiyomizu-dera, Kyoto Imperial Palace, Nijojocho, Ryoan-ji, Sanjusangendo, Sannen and Ninen-zaka, Gion and Hanamikoji Street etc.
in any case, let me know if you need any other pointers or suggestions. like I said, I'm planning my own trip right now as well so I have a lot of the info on hand.
