On my first trip to Tokyo, I stayed at the Shinagawa Prince because of it's relatively low price, hotel amenities, and its location next to Shinagawa Station (2-3 min walk). My first impression was
What a small room!!! I also discovered that there's not much of interest for a tourist in the area.
Now that I know better, I think I would have had a better time if I had stayed at the Sawanoya Ryokan near Ueno. I would of had a better taste of traditional Japanese hospitality (mind you, it's an economy class inn so you only get economy class service). And I wouldn't have spent most of my budget on my accommodation. There are also a lot of interesting places around the area for a 1st time tourist to Japan. (Do a Google search.)
Shinjuku hotels are kind of like the Shinagawa Prince (small and impersonal) and most are farther from the station, I think.
BTW, don't spend the whole week just in Tokyo. Spend a day or two in
Kyoto if you can or Nikko, at least. I strongly recommend staying at a nice ryokan somewhere, anywhere (maybe Izu?
).