London is absolutely jam packed with accommodation. Especially around the city centre this a huge selection of places to stay. If you look at the
London Hotel page you will see the variety on offer. The busiest and most popular area (where you will find more of the attractions) is the West End, so you would be looking for accommodation there. The hotels here will all be within walking distance of the most popular tourist attractions, however, if you do need to travel a little further the
London Underground will get you from A to B easily enough.
If you are looking for the cheapest accommodation possible i would suggest you take a look at the
London Hostels page.