I'm not going to suggest myself (although I did work for almost fifteen years on the railway). But I can tell you that you're near the financial district of London and there's an excellent location that can help you with anything you'd need to know.
Liverpool Street station.
It has an Underground station, so they can answer questions about the London transport system. They also have an overground rail service that serves places like Cambridge and Stansted Airport and stations all over the East Anglia region so they can help with any questions regarding National Rail. I answered questions about rail services all over the place, not just stations we served, as a matter of routine... I guarantee they'll be able to answer any train service question you have too.
And from my experience in the ticket offices, there's nothing we haven't seen and not many places we haven't seen people from and not many questions we haven't heard before. In my experience, the only place in the world that comes close to London for not being phased by meeting someone from a new country is Manhattan. I mean, I've dated people from other continents and now I'm married to an American so they won't get awestruck by your accent! In fact, you'll probably be the fifth American they talked to today (along with one or two Canadians, the French family, that nice couple of backpackers from Australia, those German kids that looked far too young to be doing Europe on their own!...)
They'll probably tell you the best (and fastest and least complicated) way for you to get from where you're staying to Rochester is to get the train from Farringdon to St. Pancras International (the next station north, a four minute hop, it's a much larger station with a grand name because you can get trains from there to mainland Europe) and then get the train from there to Rochester. You'll be able to buy a ticket at Farringdon (or while you're at Liverpool Street rail station) that includes that change of trains (the ticket will just say from Farringdon to Rochester).
