I did the Spirit of Europe last year, so I can give you some insight into how free days work.
The distance from the hostel to city centre can vary greatly. Smaller places, like the Swiss Alps, you'll obviously be in the thick of town, but I recall in Venice and Rome we were pretty far out.
Breakfast is generally somewhere between 7-8:30, depending on how you're all getting into the city centre. For example, sometimes the coach would drop us off, so breakfast would be earlier so we would all be ready to go.
As for what people in the group want to do, you really get a mix. Some people are just keen on partying and not seeing the city, others want to see it all. Word of advice - if you really want to see a certain attraction and no one else does, just go and do it! I really wanted to see the Stasi Museum in Berlin but no one wanted to go with me, so I just went off and did it myself and I'm glad I did.
It can be pretty to pre-book tours around optionals and meals. So have a look at what else is on that day, and weigh up whether you want to do the sightseeing more or the tour you're booking yourself.