Four years ago, my grandmother turned 70 and she invited all the family to a cruise on the Adriatic Sea. It was very nice but we couldn't see the cities with time. We had a schedule to keep and I only stayed in Athens for four hours! Fortunately I could see the Pantheon.
However, last year I organized an interrail myself. My friends were very happy with me because we could see many places with a lot of time. We went to Prague for three days and we loved the city. We were in Paris, Berlin, Vienna, Milan and Venice too. We were traveling 23 days and we saw everything.
Also, I organized my trip to Ireland. I found a house to go as au-pair, a flight and that was all. I spent the best four months of my life. I met incredible people and friends for ever. One of my Irish friends came to my house on Christmas!
When I was there, in Ireland, my friends and I organized many trips. We found the hostels or the shelters, the bus (because in Ireland everything is close) and the restaurants. We had lots of fun together.
In summary, if you organize your own trip, you can see whatever you want with free time. You can meet a city what who it is, not only the principal monuments.