Do you really need a rail pass? A Japan rail pass only makes sense if you travel for example from Tokyo to Kyoto/Osaka and back in 7 days. If you only have 4/5 days you may want to consider regional rail passes such as a JR East Pass which costs $184 or you may like to consider a Japan Bus Pass (10,000 yen for 3 days, 15,000 yen for 5 days). Or you can simply choose an area north or northwest of Tokyo, travel there by train (without a rail pass and avoiding Shinkansen to reduce cost) and use local transport to get around. Rail passes are unlikely to cover local transport such as buses in any case, so I'm not sure if it's the best value.

p.s. I've just noticed the OP mentions the JR East Pass.