Tate Modern is the national gallery of international modern and contemporary art from 1900 onwards. The gallery opened in 2000 in a converted power station on the south bank of the Thames in an imposing position opposite St. Paul's Cathedral
. You can visit again and again as it's free and the modern art displays change quite frequently. You'll often find enormous installations in the Turbine Hall on the ground floor.
Right outside is the Millennium Bridge (the one that was 'wobbly' when it first opened).
Don't forget, also in London we have Tate Britain and you can take the Tate Boat between the two Tates and the London Eye.
Book a Private tour of Tate Modern and Tate Britain with Viator (Buy Direct).