London Tips:

[strangely both related to safety for this city]

Look both ways! That may seem obvious now but when you are just walking down the street your natural habits kick in and you forget you're in a country that drives on the opposite side of the road from most countries. I almost got hit by a car twice while meandering through London because I didn't look in the proper direction when walking--especially look out for the double-decker buses!
Mind the gap: you'll hear it 7,000 times on the underground, but there actually is a sizable gap sometimes when entering/exiting the train so be careful

Camden Market: a hugeeee market filled with food, shops, antiques, all the things. Great spot for lunch, right on the river.
High Tea: this is a classic afternoon to-do in England and I can't recommend it enough. Awesome experience and incredibly delicious. It can get very pricey though so be sure to pick a place that is in your budget--there are hundreds to choose from.
Euston Tap: a beer bar right outside the underground station. Tons of options from all over the world with a small inside area and outside seating as well.
Craft Beer Co.: hopping beer bar popular with the after-work locals. Lots of options, good prices

Tower Bridge: wander along the bridge checking out the view
- Be sure to snag the view of Tower Bridge from the London Bridge (the London Bridge is actually super unimpressive, but it provides a nice look of Tower Bridge)
Borough Market: a great place to get lunch! Warning: it will be crowded. Persevere and wander the stands, it is worth it!
Big Ben & Westminster Bridge: walk along the bridge between the London Eye and Big Ben for great photo opportunities of both
Westminster Abbey: a gorgeous church that is a must see!

GO TO THE WARNER BROTHER'S STUDIO TOUR!!! All caps + 3 exclamation points = I cannot recommend this enough. It was one of the best days of my life and I quite literally cried at the end.
King's Cross: Platform 9 3/4: I was there in the evening and waited approximately 15 minutes to get to the front of the line, but the folks working said they've seen the line take over an hour, so be prepared. Get your picture pushing your trolley into the wall!
Millennium Bridge: the bridge getting destroyed during the opening from the Half Blood Prince
Tour For Muggles: Harry Potter Walking Tour. I had extremely high expectations and it didn't quite measure up, but it was still very cool. The Ministry of Magic, Millennium Bridge, and inspiration for Knockturn and Diagon Alleys are just a few of the stops along the way.

Granary Square: go sit by the river and hang out with the locals. There are food trucks nearby usually as well!
- You can walk along the river from Granary Square to Camden Market!
Shakespeare's Globe: either see a play or just check it out! You can't go inside without tickets but it is still cool to see. It is located right between the London Bridge and Millennium Bridge.
Picadilly Circus: London's version of NYC's Times Square. Lots of restaurants and shops, very busy area. If you're on a budget avoid eating in this area.
The British Museum: Free, but mediocre in my opinion. Extremely large and covering a vast expanse of time. You can see the Rosetta Stone here!
The Grapes: Classic English pub owned by Gandolf from the Lord of the Rings. Very local and cozy.
The Shoreditch Neighborhood: artsy, 'hipster' area with art on the walls, coffee shops, and all things trendy.
The London Eye: London’s giant Ferris wheel that is definitely worth seeing, but quite pricey if you actually want to jump on for a ride.
St. James Park: near Parliament Square, a very large park to enjoy a picnic in.
Buckingham Palace: the changing of the guards and the changing of the horse guards are both incredibly popular, be prepared to get there very early to get a spot that you can actually see from!