I've no idea why Afcjan has suggested a 4 zone card. All of the main tourist attractions are within Zone 1. Further, you don't need a weekly card, since a 3-day one will suffice.
There's not a 'Zone 1 only' 3-day Travelcard, so you'd need to buy the 'Zone 1 & 2' version, which costs �18.40. It's valid for unlimited travel on tubes and buses, at any time.
The alternative would be to get an Oyster card. These are like pre-paid debit cards. It costs you �3 deposit to actually get the piece of plastic, then you 'charge it up' with however much you like. When you board a bus, you touch the card on the reader next to the driver and it deducts �1 from your available credit. When you use the Tube, you touch it on the reader (to open the gates) at both your starting and end stations. The amount deducted from your available credit varies depending upon which zones you've travelled through but, if you remain within Zone 1, it's �1.60. However, if you remain within Zones 1 & 2, the total amount deducted in one day won't exceed �5.10 (if you only travel after 0930) or �6.70 (if you travel during the morning peak period).
If you expect to visit London again, an Oyster card might be best. Otherwise the 3-day Travelcard might be best. One of the best ways of seeing London, though, is from the river. (I thoroughly recommend the short trip from Tower Pier to Westminster Pier, or vice versa. You get some excellent views of some of the main tourist sites). If you show a 3-day Travelcard, you'll get a third off the fare on any scheduled river service. (You don't get that discount with an Oyster card).
http://www.tfl.gov.uk/assets/downloads/your-gu ide-to-fares-and-tickets-Z-1-6-02-01-09.pdf
Chris