First time to London, arrive late June for three days.

Rick's At a Glance list for London prioritizes most of the major indoor attractions, but the guidebook (either full-sized or condensed pocket-sized) covers much more, in detail, including historic and scenic walking routes. On the same page link, "Listen" includes audio recordings that go with some walking routes and museum tours and "Read" includes magazine-style articles, etc.

As Emma has pointed out, one person's "must see" isn't for everyone. What are you interested in? London is packed full of museums, landmarks, culture, history, art, food, experiences....all far too much to list here, many of which could be of little interest to you. My "must see's" and my wife's "must see's" would be completely different so my advice would be to search out some websites on London (there are many), look at what's on, what's recommended etc and build an itinerary that interests you. Why risk taking advice on something to see in so short a time from a complete stranger who knows nothing about you and your interests?

While I agree you need to go with what interests you, I can add a few Must do things:

• The British Museum: Does not matter what you like, must go here, spend most of a morning or afternoon, if you say you have no interest, then why would you even travel. It is even free.
• Do a long walk, starting at Big Ben, around Westminster, up Whitehall to Trafalgar, through Covent Garden, up to St Paul, then from London Bridge down the South Bank. Lots of things to see along the way, could do a whole day on this or break it up.
• Tower of London: Though I avoided this place on a couple trips, if you read up on it, or see some of the BBC shows on it, then it is a worthy stop.
• Hit a market, the Borough Market is great, Portobella Road on Saturdays, Camden market complex, plus several other great ones.
• Hit at least two pubs a day, 3-4 is better. A good Fish and Chip place is an acceptable substitute.

From there, you can fill in with stuff that appeals to you. Keep in mind many museums are free, so even a quick pass through is worthy, Churches (St. Paul and Westminster) are expensive, but for many are worth it (For me, Westminster more interesting than St. Paul). The London Eye...meh, River Cruises, sure, but not high on the list.

Look at the different sites on Youtube.

Just wanted to chime in that some of the fun of a visit to London is just wandering about and seeing unexpected spots, etc. on the way to something else! If you pick a few majors sites that you like, also take some time to just wander a bit. One time we took the Tube simply so that we could get to Southwark and then cross the Millenium Bridge over to St. Paul's cathedral: the fun time we had seeing the market, Southwark Cathedral, the Golden Hind, etc., etc. along the way--none of which I'd really thought much about before hand. Have fun!

Well I am pretty agreeable but I do believe that there is a way you can see all the 'must-see' sites over three days. Try taking a bus tour. My favourite is the classic tour which is brilliant (or was when i did it last year). You could also check out the various guide of Ricks which I find trusty sources of information.

In Paul’s post above he mentioned Portobello Market on Saturday’s I agree, but I wanted to add that a walk down Portobello Road any day is fun. Also, great area for taking pictures.

Of course it depends on what you like.

History: Tower of London, British Museum, Cabinet War Rooms, Imperial War Museum, British Library. At the Tower, take the free Beefeater Tour.

Art: National Gallery, British Museum

Churches: Westminster Abbey, St. Paul's Cathedral. The audio guides available at each are excellent.

The long walk Paul recommends is excellent. Rick Steves' London Guide also has some self-guided walks that are a nice way to string together many sites.

London Walks does several excellent walks each day and are very reasonably priced. Lots of fun. The evening walks are a fun way to extend your day.

EDIT: I would not waste half a day at the Changing of the Guard. it is a snoozefest.

Stay very central and with good access to the airport you are using. Clever lodging location will increase sightseeing time 50%.