I prefer to stay in "weekly mansion" places. They are much cheaper than large hotels and most have something resembling a cooking area if you want to save some money by eating some meals at the hotel. When I used to travel for work, I always stayed at Weekly Mansion Akasaka.
It's in a fairly lively Koreantown area, 5 min walk to Akasaka station and they have english versions of all the hotel paperwork in case you can't read and write in Japanese. There's a Poplar convenience store just around the corner and even a wine bar within a close walk. Most Weekly Mansions will not require you to stay an entire week, but you should ask just to be sure.