If you are going to use the tube get an Oyster card as its a rip off otherwise – The tube is bloody expensive for visitors these days so I would do teh following:
Buy an Oyster – An Oyster card https://oyster.tfl.gov.uk/oyster/entry.do is a card you scan on buses and tubes to get on – They are £3 but thats refunable when you give it back or just keep it for the next time you visit
You can then put money on it and pre pay which means each journey is cheaper than buying a paper ticket – It also has an auto daily cap which finds teh best fare for you if you travel a lot that day = see more here http://www.tfl.gov.uk/tickets/oysteronline/2732.aspx
OR
if you are going to be here quite a few days buy a weekly travel card – You can do this on an Oyster or just get a card one (no id needed for this) – The cost for a zone 1 – 2 is £25.80 http://www.tfl.gov.uk/tickets/faresandtickets/seasontickets/4805.aspx
Although the tube is at first a little daunting once you get used to it it is very easy anda hell of a lot faster than taxis on most occaisions. The good thing about being near hammersmith is that it has quite a few lines out of it District will take you SW or onto the Cricle line for Victoria, etc plus Earls Court for IGE/ICE, Picadilly will take you staright into town and Hammersmith and city line takes you aroudn teh north side of teh circle line and into the city =- Plus of course you can change anywhere