Recommendations!

I am living in a share house in Tokyo for 2 months in order to do an internship. This is my second time in Japan, but last time I was here for a leadership/exchange program so all I did in Tokyo was visit companies and network. I've been here for about two weeks, and I'm already experiencing burnout which I guess it part of cultural shock. I like most aspects of my internship but I'm feeling tired of the routine of waking up, going to work, coming home to my share house, sleeping, repeat. Does anyone have any suggestions for how to get out of thus rut? Similarly, I heard one way to fix this is to just get out and have new experiences, but I'm having trouble figuring out what to do. I want to avoid tourist-y areas in hopes of some more genuine experiences and I'm having trouble finding such things. I'm really seeking to practice my Japanese and connect with new people. Overall I just want to learn as much as I can! I'm 18 years old and originally from Denmark if that helps at all.

Thank you so much for any advice you can offer!

Think about something that you like to do anyway. Eg in my case that’s cycling. But in your case that might be something very different and then see how you can implement this in Tokyo.

For meeting people try Meetup. And even if you are not too interested in that specific experience, just sign up. It’s about getting you out and enjoy time with others.

For less touristy places you can even find them in Tokyo. Even here in JG if you drill down through the Tokyo pages areas come up that are much less touristy. Eg Shibamata
http://bicycletraveljapan.blogspot.com/2019/04/gw-2019-day-2-shibamata...

Or if you have a bit of money / time to get out of the city, try Chichibu and some light hiking. Eg to the temples around Urayamaguchi.

Look out for local Matsuri. In subway stations they are often announced.

Try to remember why you wanted to come to Japan and see if there is something on those interests you can implement.

Go and relax in a local sento , super-sento or onsen. Here my personal favorites: http://bicycletraveljapan.blogspot.com/search/label/Onsen+Practicaliti...

And well , an internship is work. So if from Monday to Friday you hardly do anything else than wake up, breakfast, go to work, work, ship for dinner, come back home, some TV and to bed, well, that’s what worklife is. In Japan sometimes you get a drinking party in between , but that’s essentially how Mondays through Fridays work. In most parts of the world and a bit more so in Japan with the overtime work culture and the long commute.

I agree with LikeBike's suggestions. Life is what you make of it, but you must be prepared to do the hard yards both workwise and socially. If you don't make an effort you will stagnate.
I lived 40 mins outside of Tokyo for four months on my own helping out a friend who lost his wife. On spare days I just jumped on local trains and got off to explore the communities surrounding the stations.
Having been to Japan previously, you should have experienced some of the culture both inside and outside work hours. There are a multitude of things to do (even by yourself). Go and enjoy.