Good for you; I'm jealous! I know there are a lot of people who approach rail pass decisions by "doing the math" and only buying a JR pass if they will at least break even on a fixed itinerary that they come up with based on decisions other than transportation. But I am more inclined to come up with an itinerary based on what I can do with a JR pass. (I would spend months thinking about it and weeks fine-tuning it, so the idea of coming up with a plan in just one day makes my head spin, but I'm sure you will have fun.) What I especially like to do is make one or more home bases using carefully selected hotels that are near a major JR station (usually one where a shinkansen stops). With a week or more I would pick at least two cities. With a three-week pass maybe four or five? I might do some sightseeing in the city where I'm staying, but I always take numerous day trips. I don't completely understand why so many people are dead-set against "long" train rides, as I do not find them unpleasant at all. To each his/her own. One of the great things about rail passes is the value you can get by making round trips from a home base in one day, as opposed to point-to-point travel where you just go from one city to another (and have to change hotels each time).
The sky's the limit, but with a three-week pass starting out in Tokyo, I'd probably confine myself to either Kyoto and points West/south (I particularly love Kagoshima!) or else Kyoto and points east/north (possibly as far as Sapporo), and maybe spend a week in Kyoto and the rest in two or three other cities. Day trips every single day would get to be a bit too much, so pick cities that are fun to just hang around. For that reason, medium and large cities can be a better bet. Maybe Fukuoka, possibly Hiroshima or Okayama. Definitely Osaka or Kyoto. I thought Himeji was actually a nice place to stay, with lots of good restaurants. The hotels there were surprisingly affordable. None of these places are lesser-known, of course, but they give you a lot to do without leaving the city as well as many options for medium and long day trips. (Okayama is particularly good for that. I have made numerous Shikoku day trips from Okayama, and also one to the Adachi Museum in Yasugi, one of my best day trips ever. Of course, you can easily get to Osaka and Kyoto from there as well, if you end up not sleeping in those cities but wanting to sightsee in them.)
Since you haven't been up north yet, maybe Tohoku would be nice? I have found Sendai to be a good "home base," with numerous easy day trip possibilities. Lots of good places to eat in that city, and the Tohoku shinkansen is fast and scenic.
The Hokuriku Shinkansen is another possibility. Have you considered Kanazawa? Nagano is actually not a bad base for day trips, as you can get to Kanazawa easily but also Tokyo, which gives you a huge reach to avoid bad weather or seek out special events (although so many of them are cancelled right now). There are several nice places close to Nagano as well (Togakushi is my favorite; Obuse is also nice, and there's always the monkey park). Anyway, if you are heading west from Tokyo, consider using the Hokuriku shinkansen either on the way out or the way back.
Finally, if you like train travel, consider the JR sightseeing trains. They are an experience in themselves. At present, many have limited schedules because of coronavirus, but they are starting to resume more of them. I'm not up on the current offerings, but you can find a lot of information online. The respective JR companies have special pages devoted to them. (If it's in English just be sure to verify details before you book, as JR tends to not update its English pages very often and the information on them might not be current at all.) I particularly like the ones in Kyushu... Besides the JR trains that are particularly oriented to recreational outings, there are a lot of good limited express trains that can give you a fun and scenic ride. A good example is the Marine Liner from Okayama to Takamatsu. This is a swell ride, not terribly long, and Ritsurin Koen in Takamatsu is worth a trip even if that's all you do there.
As for Hokkaido, I guess I would tend to avoid a spur-of-the-moment trip there without much planning. Sapporo would be okay for that, but Hokkaido is really a gigantic place, and getting around by JR severely restricts you. The trains don't run very often, and the distances are vast. You could end up stuck in the middle of nowhere with not much to do, is my sense. (Admittedly, I haven't spent much time in Hokkaido myself.) I definitely would not limit a trip there to the winter season, but I would approach it with a fair amount of research under my belt. Just my own opinion.