To throw a wildcard in, staying in Shibuya and Shinjuku are the noiziest and busiest places, pick a quieter nearby yamanote line station and stay near there. It won't take you above 15mins on the train to get into that area, and as said they two districts are next to each other and you can easily hop on a train or even walk between them.
I like the toyoko inn chain, they are all on google maps so google the yamaote line and look to see which of their hotels is hear by.
I think about budgeting a lot though, maybe cost is of no issue to you?
Regarding the JR pass, worth it if you intend to travel between cities a lot, if you just want to travel a lot around Tokyo are in the day there are many different types of "day pass" for the systems, some let you use trains, some trains and subways, some trains, subways and even the dreaded, confusing Japanese bus
