For Edinbourgh, there isn't a whole lot there. I would definatly go to the Castle, and if you want a good view of the City there is a Hill, i can't exactly remember where it is. You can see it easily in two full days.
For London, everything is fairly close toghether. A must see is the tower of London, and then go to the tower bridge, if you want a nice view along the Thames, you can go up to the top of the bridge and walk across the walkways, it was neat. London is very expensive, but it is easy to do everything in 3 days, because the subway is very easy to figure out.
Hope this helps, its hard to do must sees for Europe, everything is must see :)