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/) is also a favourite of mine). Out of town (near Milton Keynes) is the National Museum of Computing (http://www.tnmoc.org/) including the Bletchley Park codebreaking site.
Between Tower Bridge & HMS Belfast lies City Hall, which does little beyond looking weird (http://en.wikipedia.org/wiki/File:CityHallLondon2007.JPG), although it occasionally hosts exhibitions.
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/) is central, small, and partially closed for renovation; it currently goes as far as the Great Fire in 1666. The Museum of London in the Docklands (http://www.museumindocklands.org.uk/) is much bigger and newer; it focusses more on the Thames but I reckon it's also better for general history.
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/parsingphase/664727004/), and it's somewhat outgrown by nearby tower blocks although the view's still good (http://www.flickr.com/photos/parsingphase/664727742/)
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/parsingphase/664726390/), and also a very good free art museum.
London's other cathedrals include Southwark (http://www.flickr.com/photos/parsingphase/663869585), situated next to the gastronomic heaven of Borough Market (http://www.boroughmarket.org.uk/), and (presumably the oldest, if no longer strictly a cathedral), Westminster Abbey (http://www.westminster-abbey.org/), consecrated 1065 and, together with the Palace of Westminster (where the government sit), a UNESCO world heritage site.
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/) is an astounding Byzantine building situated a little way south, near St James' Park and Buckingham Palace (http://www.royal.gov.uk/TheRoyalResidences/BuckinghamPalace/BuckinghamPalace.aspx). FWIW, most Londoners consider Buck House (as they call it) to be overpriced and over-busy, so I'm not sure I'd recommend the internal visit.
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/trafalgarsquare/visit/index.jsp), with Nelson's Column, the National Gallery (http://www.nationalgallery.org.uk/, free I think, has a very nice cafe too), and National Portrait Gallery (http://www.npg.org.uk/) (also the Embassies of Canada and Korea, the latter often holding exhibitions).
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.