So now I live in Japan. I’m loving it so far, it’s just that the Nagoya region really seems to be boring.
I will be checking out the obvious touristy things, such as museums, the zoo, the aquarium… but isn’t there anything else a bored gaijin would love?
If the Shinkansen weren’t so expensive, going to Tokyo/Osaka/Kyoto once in a while would be great.
Leave. As quickly as possible. 
Hasn’t improved much, I take it. I was in Nagoya as a student 15 years ago (Nanzan U), and honestly the best advice is to get away. It’s winter - go to Gifu, the mountains are gorgeous. Or to Kanazawa on the west coast. If the Shinkansen costs too much for you, take cheaper trains to Kyoto or Osaka (slower but if it’s anything like when I was there, the price differences are enormous).
It’s a great problem living in a city that we bombed so thoroughly (if justifiably) - there just isn’t much left that’s interesting.