I think Karuizawa is the perfect day trip by bullet train. Lots to do and beautiful in all seasons!
And also Kyoto is also available by day trip. Or if you are aiming to have the Shinkansen experience, Odawara is pretty closer from Tokyo and nice and cozy place to visit!
I recommend,you should go to NASU.
It tkakes about one& half hour by SHINKANSEN from Tokyo.It is cooler than Tokyo.
Especially in summer , you can enjoy nice vierw ,cool air,nice foods,shopping,fruits huntings and so on.
Many people use Shinkansen from Tokyo to enjoy ski day trip in winter. They head to GALA Yuzawa or Naeba Ski Resort from Echigo Yuzawa Station. The station is also very nice because there are lots of shops, including Japanese sake tasting shop. At the shop, you can try various Japanese sake and buy a bottle you liked :) (Echigo Yuzawa is in Niigata Prefecture and Niigata Prefecture is famous for rice, and Japanese sake!)
Nagoya is also only about 1.5 hours away from Tokyo. You can find unique local cuisine there. Such as Miso-Katsu (deep-fried pork tonkatsu seasoned with thick miso paste), An-toast (a toast with red bean paste!) etc. You should visit Atsuta Shrine. It's a beautiful shrine with forests.