what is the most economical pass i can get

I will be arriving in Tokyo(Narita Airport) on 28Dec 2018, travelling by train to the city, Shinjuka station. Staying 2nts and then travelling on to Nozawa Onsen by train and staying 6nights. Can you please tell me if the JR East Pass 5 day validity(Nagano, Nigata area) will cover my trip from Narita Airport-Nozawa. Will I also have to by a separate ticket back from Nozawa - Tokyo (Haneda Airport) which is where we will be leaving from. I would just like to know the most cost effective way is of doing this trip by train.