2. Book accommodation after exploring the subway/train lines - you can save a lot of money.
Another thing I’d really recommend is that you don’t go ahead and simply book an apartment “somewhere in the center of the city” but instead explore your subway/train options first. I would suggest first taking a look at where your university/school/company or most of the desired tourist destinations are, and which subway/train stations are in its vicinity.
Here is why. When we were booking a place with Sakura House, there was a really neat apartment near the center of Tokyo that cost the same as the room in the share house that we later took. Obviously, our first thought was to take the apartment, but since it did not have a direct subway/train connection to most of the places that we wanted to visit, we did a bit of transportation fee calculating using this website:
https://world.jorudan.co.jp/mln/en/?sub_lang=nosub
Here is what we discovered. If we stayed at the share house next to Yamanote Line (direct connection) we would only have to pay about 200 yen in one direction for most of the places that we wanted to visit. If we stayed at the apartment (forgot the location, but we’d have to transfer once or twice every day), we would have to pay between 600 and 800 yen in one direction for most of the destinations - that’s three to four times more!
That is why, if you are on budget, I would really suggest trying to book a place withing walking distance to the train station that will have a direct connection to your most frequented places. For tourists in Tokyo who want to do a lot of sightseeing, that is most likely the JR Yamanote Line.