All the Historical Royal Palaces (http://www.hrp.org.uk/) are worth a look, but if you're seeing one, the Tower's certainly a good choice. The Crown Jewels are certainly worth a look. Nearby there is of course Tower Bridge, which is a great sight in itself, and gives a great view from the top (although it costs to get up there). You can also see the engine rooms of the bridge, with the original Victorian steam mechanisms (although these are no longer used). I think it's a couple of quid, and it's really worth the few minutes it takes if you happen to be crossing the bridge.
Tthe Tower fascinating and would go again. Tower Bridge was closed (to tours) when we were there.
Across the bridge, just about opposite the Tower, is HMS Belfast, a 2nd World War Cruiser that's now a floating museum (http://hmsbelfast.iwm.org.uk/) (not everyone's taste, but I have an interest in Military History, and I'm a member of the Imperial War Museum, which also runs its main museum south of the river, and the Cabinet War Rooms from where Churchill direct British operations in WW2. (The National Army Museum (http://www.national-army-museum.ac.uk/
Between Tower Bridge & HMS Belfast lies City Hall, which does little beyond looking weird (http://en.wikipedia.org/wiki/File:City
Other museums worth noting in London are the V&A Museum of Childhood (http://www.vam.ac.uk/moc/) (in East London), the Natural History Museum (http://nhm.ac.uk/) & Science Museum (http://www.sciencemuseum.org.uk/) (these last two are both next to the V&A and, I believe, free). There are two museums of the history of London itself (well, the same museum on 2 sites) - the Museum of London (http://www.museumoflondon.org.uk/)
Regarding the Great Fire of London, the Monument (http://www.themonument.info/) to the fire stands near London (not Tower) Bridge; you can climb it internally but it's very tight and windy (http://www.flickr.com/photos/parsingph
London's St Paul's cathedral was probably the most famous building destroyed by the fire; it was rebuilt in a very different style and has some of the most impressive architecture in London (http://www.stpauls.co.uk/). It stands just over the river (via the Millennium Bridge) from the Tate Modern (http://www.tate.org.uk/modern/), a very different piece of architecture (http://www.flickr.com/photos/parsingph
London's other cathedrals include Southwark (http://www.flickr.com/photos/parsingph
Chris and I spent several hours wandering through Westminster Abbey and it's fascinating. The Palace of Westminster, of course, is where you'll find Big Ben.
Conversely, the Catholic Westminster Cathedral (http://www.westminstercathedral.org.uk/
The Queen is usually in Scotland during the last week of June/First week of July and during that time Buckingham Palace is open for tours. Holyroodhouse, the royal residence in Edinburgh, is closed. I don't recommend attending mass at Westminster Cathedral as, even with a modern sound system, we couldn't make out what anyone was saying.
Just north of Westminster is Trafalgar Square (http://www.london.gov.uk/trafalgarsqua
There's a number more palaces in and around London; one of the most intriguing is Eltham Palace (http://www.elthampalace.org.uk/) which is part Medieval, part Art Deco.
Anyhow, this city can keep you busy for months if you let it - I haven't even started on the Markets, Theatres and Art Galleries, but I figure the above should be interesting for a while.