You can do one of those tours that visit a lot of countries in a few days. We did a 12 day Cosmos tour years ago and saw 8 or 9 different countries, it was great. They arranged all the tours, excursions, hotel and transportations. One of my favorite trips ever

I lived in Europe and even took tours from time to time. The advantages are that you get to see more in a shorter period of time and do not have to worry about finding a hotel room or museum tickets (yes, you should make reservations for those--lots of people do not realize that, but the alternative is a very long wait.) Sometimes, a tour is cheaper than doing it on you own.
However, my favorite trips are those when I went to one or two places and wandered. It depends on lots of different factors--and your personality and budget.

Personally, I would not suggest the one listed above. But, that does not mean it is bad-- I would recommend a tour of one country, however. Just be sure there is plenty of "free time" to roam around. Be advised that some of the tours have stops that are designed to get you to spend money: a pottery factory, lace factory, etc. Sometimes these stops are out of the way and you cannot escape the pitch.

Venice was nice for a day or so but I agree that it seemed a bit like Disneyland to me. Very few Italians actually live there. Its a tourist destination. I liked Florence and Rome better. And Siena is lovely too.

London! I didn't like Venice - maybe I was tired coming from a 15 day trip to Rome and Tuscany, but I thought Venice was a tourist trap, with nothing really authentic. Even the painting of the buildings was fake, to make it seems you are around old/charming architecture.

I just didn't like it.