You need a UK Electronic Travel Authorisation (ETA) before you land. Use the gov.uk ETA app to apply (super easy). It costs £20 and it says allow 3 days to process but once I forgot to do it and did it when I landed and it was done by the time I’d walked to immigration. Valid for 2 years (or until your passport expires)
Fastest: Heathrow ExpressBest balance: Elizabeth lineCheapest: Piccadilly linePeople say not to take the Heathrow Express because it’s kinda overpriced (£35 return ticket) but honestly it’s so convenient (15 mins vs like 35) it may be okay to pay for it. It’s also cheaper if you book 2 weeks in advance (like £10 I think). I’m like 50/50 on whether I take it or not (I mostly take it on the way to the airport because I’m late or something). It takes you straight to Paddington which is central enough to get a tube or an Uber afterwards.
If you decide not to take it, take the Elizabeth Line to somewhere central (Paddington, Bond Street, or Tottenham Court Road probably) which will cost you like £12.90 and take 30 mins. Then take a black cab or Uber to the hotel (especially if you have a lot of luggage).
The cheapest option is to just take the Piccadilly line (£5.80) which serves the airport but it'll take around 50 mins to get into central London and is just such a slog. Not ideal for luggage either since it's just a normal tube line. Only really worth it if it’s gonna take you right to/near your hotel/AirBnB and you don’t mind waiting.
Use the same card for every trip. Tap in and out on the Tube and Overground; tap in only on buses and trams. They charge you more when you cross zones (e.g. if you’re going to Wembley or O2 for the concert) but other than that you should mostly be in Zone 1 anyway.
Try to know walking routes beforehand if you’re in a busy area. There are phone snatchers and you don’t want to be caught staring at your phone (speaking from experience unfortunately 😔).
Book the Sunday roast, play or show tickets, Westminster Abbey, Tower of London, museums with special exhibitions, and cocktail bars if they take reservations.