London

Tower of London - Do one of the tours led by the Beefeaters there, well worth it rather than trying to do self guided, you learn a lot more.

Westminster Abbey - Again, take one of the tours by the volunteer docents there. I think there may be a small fee and you may have to book in advance, but it’s well worth it.

Covent Garden - Go to watch the street performers. The pub there has a balcony, if you’re lucky or early enough to get a seat on it, it’s a great place to have a pint and watch the performers.

Leicester Square - If you’re into theater, there’s a half price tickets booth for unsold tickets for the same day. You likely won’t see tix for major broadway type productions that are well sold in advance but you can get still get some good stuff. If the weathers nice I highly recommend the Open Air theater in Regents Park. You can buy bottles of wine and food there to drink at your seat outdoors while you watch the performances.