Well Ireland might not be for you if city traveling is your thing. Dublin isn't very big and the next best "city" we saw was Galway, which was great, but is more of a college town with only 75k people. 4th biggest Ireland. Our favorite parts were the natural beauty of some of the country. An amazing variety of landscapes in small areas. You could fly london to Shannon and see a decent amount of the west coast driving(best way to see the ireland) for a few days. Google the ring of Kerry for examples.
Tons to see in London with tower bridge, Big Ben, Westminster, museums, St. Paul's, Hyde park, sport venues, or just wandering the city. Harrods is worth a visit. Some great day trips easily done by train in order are Windsor, Brighton, and Bath. In my experience London is more about the history and the culture of a huge mixed city and ireland is more about the natural sites and breathtaking views.