This connection time is problematic even for getting into Narita town. Immigration waits can be 60 minutes, although they also can be 5 minutes. Checkin time is 2 hours before departure unless you have status or are flying C/F. Even then, I'd suggest 80 minutes since there can be a line for outbound passport checks (although if you are late, they will usually pull you out of the line for that one).
The Keisei line train between Narita airport and Narita town runs about once every 20 minutes.
So if you check out immigration and there is no long line, you might consider trying it. You would have about 3 hours once you pass immigration. You need some Yen, preferably from the ATM, then buy a ticket to Narita downstairs. You can change the leftover Yen at the bank at the airport upon your return.
Complete details on what to do are in Mike Newman's Narita layover page, which is back online.