The Federal Reserve Bank of Chicago has a Money Museum that anyone can walk into and tour during regular business hours:
The Federal Reserve Bank of New York requires you register up to 30 days in advance. In theory you could probably register the day before but in practice it fills up within 30 minutes of becoming available. Tours are done in groups but the groups consist of everyone who register and you need not register with anyone else.
The Federal Reserve Bank of San Francisco, however... it looks like they only allow group tours. You don't register individuals - you register groups - and if your group is less than 15 people you won't be granted a tour. To top it off they don't appear to do very many tours a year. Maybe one or two:
So what about other federal reserve banks / branches? Are there any others that solo travelers could see?