1 month visit to Japan!

Hi!

I am a student that is going to visit Japan during May for my graduation trip! (:

My current itinerary is:

Arrives at Narita Airport -> Proceed to Osaka -> Explore Osaka, Kyoto, Kobe, Nara for 1 week -> Proceed to Yokohama and explore around for 5 days -> Proceed to Tokyo for around 1 week -> Narita Airport

Hence I will be staying in Osaka (1 week), Yokohama (5 days) and Tokyo (More than 1 week). I was thinking of getting a rail pass for the first week? That means it will only cover the cost from the airport to Osaka and areas around Osaka. I am planning my trip with a very tight budget so any suggestion will be of great help!

Thank you so much (: