@em got me super nostalgic for London. @caraaklark is an ideal travel buddy FYI and did most if not all these things with me.
  1. Get a bowl of ramen at the Wagamama in Southbank. This is a chain restaurant, but I like this location best because of the outdoor seating by the river.
  2. Wander around Marylebone and weave in and out of the shops. Go to Daunt Books and pretend its the library of your dream house. Afterwards get a strong pint of cider at Coco Momo.
  3. Covent Garden is perfectly fine in the daytime but avoid at all costs at night. The bars and clubs there are way overpriced all tourist traps. @caraaklark and I made this mistake so you didn't have to!
  4. When the tube shuts down you can rely on the buses, just make sure you hail them down! Otherwise they will assume you're waiting for the next bus and keep going.
  5. Dedicate a whole day to wandering around Cambridge. Haggle with a vendor over the price on a vintage Givenchy dress, get Moroccan food, smoke some hookah.
  6. Avoid spending money on stores that exist in US (H&M, Zara, etc.) but don't let it deter you from walking down and admiring Regent St.
  7. On Sundays, walk down Brick Lane past all the beigel and Indian restaurants until you hit the vintage market. When you get hungry go to the food market next door. There's a good Ethiopian stand if you can find it but £5 should get you a decent plate of anything.
  8. £5 grilled cheese at Borough Market paired with mulled wine by the Stoney St entrance is a great way to warm your insides on a chilly day. Walk alongside the Thames, sit outside by the Shakespeare Theatre and people-watch as you snack away.
  9. Go to the BFI and watch a screening or two or three. They always have a great program and selection of films. I got a bit homesick when I watched Manhattan there with Kara but only for a little bit. I also saw Charlotte Rampling give a talk there. She is the epitome of elegance.
  10. Stick to tea. Nordic Bakery is a cool cafe where you can get a decent cup but that's because they're Swedish. Tea is best. Get a cup of tea from Tom's Deli at Somerset House and enjoy it on the terrace outside.
  11. Do see as much art as you can. V&A, Tate, Tate Modern, British Museum, National Gallery, etc.
  12. Shows at the National Theater or Donmar Warehouse, seeing Whose Line vets improvise at the Comedy Store, tea at the Orangery, Carnaby St., Sunday Lunch at the Calthorpe Arms on Gray's Inn Rd., Edinburgh Fringe warm-up shows at pub theaters like the Hen and Chickens, an afternoon pint and crisps at the Calthorpe Arms.
    Suggested by @Seth