If you take exit 1c after getting to Roppongi by Hibya line you will end up right next to Mori Tower along with some other cool things to see. Although it was a cloudy day, the weather itself was pretty nice and it didn't actually start to rain until later so it made for a good day.
Even though I hadn't planned on buying anything that day at the gift shop I did end up buying a few things that were pretty cool. The exhibit displayed artworks made by an artist whose signature was "Mucha" I believe (ashamed to admit I can't remember his full name at the moment) and his artworks dated back from the late 1800s till the 1930s and were quite amazing. He was from the Czech republic and some of his artwork is considered to be a national treasure.
There were paintings in that exhibit that took up entire walls and it seemed like he had the gift to design practically anything from posters and stained glass windows down to silver boxes. It was all really inspiring and since naturally no pictures are allowed in museums I've decided to upload some here that I took of the merchandise I bought. I basically just bought a couple folders and postcards that had designs that he named the stars.
He was really creative with his work as he gave the seasons (i.e. Summer, Spring, Winter, Fall) human forms of his own design as well as the stars and moon (i.e. Morning Star, Polar Star, Moon, etc.).
And of course we can't forget about lunch. While artwork is cool and I absolutely have the appreciation for it, staring at artwork for a long time makes you hungry so after the exhibit we decided to have a Japanese lunch at a restaurant called Sakura. Not only was there a discount for students on the exhibit, which cost 1,200 Yen, but afterwords we were able to use the ticket for the exhibit for discounts for food at any restaurant in the tower so that was a tasty plus!
Overall, although there wasn't much exploring involved I had a great time in Roppongi and joining a club has made studying abroad even more worth it. If there's anything I'd recommend to anyone who intends to study abroad in Japan it would be to get as much as you can out of the experience and do something like join a club! It will give you the opportunity to make more friends and also possibly even go places you normally think you wouldn't. Going places is always more fun when you have more people. Good luck!