Heathrow is the main airport for London and is to the west if the Greater London area. There are various types of public transport varying in cost. The budget minded should take the underground (tube, metro, subway) but note there are fast trains which cost more. It's not a bad idea to have a night here to acclimatise to London. There are places that you might visit from here (do your own research!) and London buses currently charge a flat fee of £2.