I'm a big fan of the Museum of London. It panders to my penchant for Romans, hosts very interesting exhibitions, and has a great app to guide you around the city itself: Streetmuseum. To mark the launch of version 2.0 of Streetmuseum, the museum has released 16 gorgeous, ghostly images of the city, merging past with present. You can look over the Thames from Tower Bridge, from the 1920s on the left and the 2010s on the right; or stand on the corner of Long Acre and Neal Street (just about where Marks and Sparks is now), looking towards Covent Garden Tube station, 2010 on the left, 1930 on the right. It's wonderful to see how much London has, and hasn't changed.
The new version of the app has had 100s more city locations added to it, meaning that you can select a destination from a London map or let yourself be geo-tagged to your present location. Then a historical image of London will appear on your screen and you can expand it to learn about where you are. Most of these are in central London, but some are in its outer reaches, too.
The photos range in date from 1868 to 2003 and were taken by photographers including Henry Grant, Wolfgang Suschitsky, Roger Mayne, and George Davison Reid.
The app is free to download to your iPhone and is available now.