We like to combine an organized group tour with independent travel; for us, it's the best of both worlds.
This year we did two RSE tours: Loire to the South of France, and Best of South Italy. We arrived a week before the first tour, splitting our time between Paris and Chartres, where the tour began.
After that tour ended, we spent the next 10 days on our own, splitting the time between Venice and Rome, where the second tour began.
And after the second tour, we stayed in Naples an extra couple of days, then spent 10 more days split between Siena and Bologna, on our own.
That made for a long trip, but it was wonderful. We always take on about 10 days after a tour, and always arrive at least 3 or 4 days early. We still get to plan our free time, but have the luxury of letting somebody else do the basics of housing, meals, and transportation for at least part of the time.
I will also say that one of the things we like about Rick Steves tours is the generous amount of free time on most of them. We have taken a couple that we thought were overscheduled, but most of them have plenty of free afternoons and evenings. Go look at the tours he offers, pick any one, and carefully read the itinerary for that tour. Then check out a couple of others. You may find something that fits your needs. Follow the links that Kathy posted upthread.