I’m not sure if my first trip to London can be considered a visit given I had only half a day to see the city.
I didn’t remember anything except for the arrival at the busy Victoria train station. Then I hauled my over-packed backpack from street to street around the station looking for accommodation. Everything was booked out. The available ones were too expensive for a student who had just return from an internship in … Eastern Europe. I had vague images of the Thames and the London Eye. I might even ride it without remembering anything. I remembered joining a group of Malaysian businesspeople to walk around the red-light district and then ditching them later not having enough energy and mood to socialize with complete strangers.
Visit the museums is a must when you are in London. Most of them including the major ones are for FREE. The collections and paintings in some museums I visited are of absolute quality, worthwhile of your time. The only minor problem is that there are many museums worth seeing and scattered around in the city in addition to the size of each one.
Some open very late (until 10 or 11 p.m. on particular days); you might want to note down the hours to check them out after sight-seeing the city.