I don’t really know how many days you have free or what your tastes are, but here’s a few ideas that come to mind. The first would be 3-4 days, three days of proper sightseeing and one day for transit plus a quiet day at a geothermal hot springs town. You’d be staying all 3-4 nights in the same place, a small city in the mountains, and would take the first full day to visit its temples, sake breweries, historic buildings and other sites. I personally recommend staying overnight at a ryokan, a traditional Japanese inn, for a different hotel experience!
The second day could include a visit to a nearby secluded town that still preserves its traditional farmhouses with thatched roofs and old way of life. Another day for a trip to a famous garden and an old geisha town, alongside a cool contemporary art museum. If you have the time, there are other small towns in the area which could easily be included in the itinerary.
If you have more free days, this can be expanded to 6-7 nights (or more) and move your base to another city a couple hours away. This plan could also include visiting wild monkeys that bath in hot springs, a famous wooden castle, a wasabi farm, rice fields and/or a mountain town used as the ancient highway between Kyoto and Tokyo. If you want more, a day to the base of Mt.Fuji to see Japan’s iconic symbol is also nearby and well worth a visit before arriving back to Tokyo.
As you can see, this area is mostly in the mountains, it may still be a bit chilly in March so we can find a different area if you’d prefer to avoid the cold, and is quite laid back with plenty tradition, culture and nature. Of course, these are just ideas and anything could be taken out or changed around to what interests you most.
Food in this area is very unique and worth trying, so I’ll point you to my favourite restaurants too! Here are some examples of regional specialities around in March: