Got Any Good London or Dublin Recommendations?

My husband and I are very close to heading off for London and Dublin for a little while (a few days in each city), and would love any recommendations of "can't miss" things to do, see, eat, etc. that you might have! We are planning to be pretty low-key on this trip and not try to wear ourselves out doing everything there is to do, but I know many of you have tons of experience in these cities so I'd love to hear about it. In fact, I just re-read some of the London suggestions from the comments in this post last year and have some of them on our list for this go 'round.

Our kiddo will be staying safely in the US while we are away, so this is an "adults only" trip. We both were in London during the Olympics last year, and I had been to London before that, but this is the first time to Dublin (or Ireland for that matter) for both of us. We have a few things planned, and a few reservations already made, but are still looking to add to the list.

So, if you have some suggestions to share, I'd love to hear them! Hopefully some of these ideas can help others who might be planning similar trips as well. Thanks in advance, and can't wait to share the details about how our trip that was made possible by miles and points!