How long are you going for?
If for a couple of weeks it will give you a good opportunity to travel around the country fairly easily.
As a foreign national, you can purchase a Japan Rail Pass.
This will give you unlimited travel for a set period on all of the JR lines and all but the fastest bullet trains.
This has to be purchased before you go, and redeemed at one of the JR counters (which they have at the airport) you will need to carry your passport with the rail pass to use it.
February will probably still be a bit cold, so take some warm clothes with you (or plan to buy out there, UniQlo is very cheap, especially tax free, I usually do this as half of my luggage is usually gifts for family).
With regards to watches there are some good pointers on
the thread I made last month. The 2 I missed out on due to lack of time was the Seiko museum, and going to see the myriad year clock at the national museum of Nature and science in Tokyo. (I'll probably plan them in on my next trip).
While there, other things to do may be to go to the sky tree building if the weather is clear, the view is amazing. There are 2 different observation decks you can go to, tickets to the higher one cost more. ( I went to the first one on new years, the queue for tickets may be quite long)
Odaiba is well worth a visit too. There is a giant Gundam there, a Toyota museum, people were test driving cars as well, though I don't know what the requirements for this are as I didn't do it. And if you go there, definitely go to the team lab exhibition.
Other than that Ueno zoo is nice, though you may have to queue to see the panda's.
If you have time I would definitely recommend Kyoto, though in February some places may be closed.
A very good resource is;
https://www.japan-guide.com/
Osaka is awesome for food. I wouldn't bother with the inside of Osaka castle as it was destroyed in WW2 and the interior is concrete.
If going to Hiroshima, I would also recommend a short ferry ride to Miyajima.
There's probably loads I have missed out, and I am sure others could help out too. (Read up on any of my recommendations, as I haven't been in February before).
Hotels don't have to be expensive, I usually just stay at business hotels as they are cheap, a place to sleep and overall tend to be pretty clean. If you want more space, then Airbnb may be a better option.
In any case plan to go sightseeing a lot and enjoy, there's a lot to do out there. Enjoy the food for sure.
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