Don't worry too much about selecting hotels. Anything above a hostel will be clean and safe, although with smaller rooms than you are used to.

Shinjuku is excellent for transportation, but it's a huge business and shopping district, and you're not going to find much peace and quiet. I do concur with the recommendation to see the view from the Tokyo Metropolitan Government building, though. The viewing areas also have coffee and souvenir shops and sometimes an art exhibit.

Shinjuku is also a good place to experience the wonders of a Japanese department store. Sure, there are floors and floors of clothes, but also a gourmet grocery store in the basement, two or three floors of mid-priced restaurants, a roof garden, and maybe a movie theater and art gallery. One feature that you won't find in Western department stores is the Japanese clothing section. Real kimono can cost huge amounts of money, but the incredible brocade fabrics and accessories are worth ogling.