The underground is definitely the best way to get around. It is the quickest and most convenient. Buses can prove a problem for tourists now because you need an Oyster card to use them (cash not accepted anymore), and black taxis are very expensive.
Easiest - Tube
Most Fun - Bus
London Bus Maps are available from Tube Stations. Nothing like sitting in the top front seat as you pass all the sites, and much cheaper than a tour! Try the number 11 or the number 6.
Always buy 'multi-zone' Tube Ticket. When last there, was staying at Hammersmith, only a little distance to its' Tube Station. The many other times', stayed about 30m from Piccadilly Station. Travel from/to Heathrow by train, too.
Loved its' versatility, ease of use, quickness of journey.....all 'systems go' for me!