V&A, for artistic stuff through the ages. The Science Museum again (because unless you spent a week in that building, you hardly saw any of it!), and on and on! The Museum of Natural History has a lot more metalwork related stuff in it too, beware of some of the funnier Bad Taxidermy on display! 😛 I wanted to get to the Museum of the Worshipful Company of Clock and Watch Makers, but it was closed. The Royal Armory Museum at Woolitch, IIRC. The Tower. One complaint I had with the Science Museum, was the atrociously low lighting levels in many of the display areas, I felt I needed to have brought a flashlight and many changes of batteries!
Best two decisions we made was firstly, to buy an advance purchase transit pass. Second, NOT buying the multi-access passes that allow you to enter dozens of different attractions, historical sites and museums, as you are gonna feel gypped, and rushed, trying to see what there is in, say the Tower, in a half day. The Transit Pass was quite cheaper to buy in advance, while the Attraction Pass worked out more expensive than simply paying at the entrance due to the need to visit two or more attractions every day to cover it's cost, which would have lead to being exhausted, tired and sore, instead of just focusing on one location at a time, which left us pretty happy we were not feeling pressures to scramble around.
We got very lucky, without intending too, as the Hotel (Citadines Trafalgar Square London) we stayed at was a tiny bit past spitting distance to Trafalgar Square, about equidistant from the Square and the riverside of the Thames, easy walking distance to the Tube and Train Stations as well as a short walk over to 10 Downing Street, Horse Guards, and MANY other notable locations.