Shinjuku is also a good spot for a trip to Hakone on the non-JR Odakyu Line or to Kawagoe on the Seibu-Shinjuku Line.
The JR Station is confusing, and there seem to be new exits all the time, but just take a deep breath and follow the signs. If the weather is bad and you want to go to one of the East Exit businesses, there's are underground walkways, one fork of which leads to Shinjuku Sanchome subway station and the other fork of which leads through a shopping arcade called the Subnade to Seibu Shinjuku Station. Really, there are underground walkways all over the place, built for the benefit of people who are transferring from one transit line to another but partly available to people who just want to get out of the rain. Even some of the hotels are connected to the walkways.