I've done 10 Rick Steves tour and 10 Road Scholar tours, 5 of them in Europe. I definitely like to arrive several days ahead of time to Europe. I'm retired so try for at least 5 nights ahead of time altho if Paris or London are in the mix then I'll go for a week to 10 days. If I don't want to spend it in the tour start city I'll at least go to that city the day before to give extra time there. On the US based Road Scholar tours I also like to arrive ahead of time. Last year on the way from Idaho to FL I got stuck in the Atlanta airport overnight in January (I knew this was going to happen) but I'd arranged for 5 nights ahead of the tour so had some time to play with.
I did make mistakes on several Rick tours when I should have planned for 2 or 3 nights ahead because there was so much to see in those towns. The tours were 21 Best of Europe, GAS and Village Italy. I found Haarlem, Trier and Padua to be filled with interesting sights that I did not allow enough time for!
As to time at the end, well, it depends on the ending point. I spent an extra night in Orta San Giulio on the VI tour and that was overkill - would have done better to use that time in Milan. On some of the other tours I had another back to back planned either with a Rick tour or a Road Scholar tour. On the Road Scholar tours, particularly ones in England, the last night of the tour is at a hotel at Heathrow so it seems silly not to just head home when you are that convenient to the airport.
I'm never ready to come back home, lol! Even after 8 weeks in Europe I'm still ready to Keep On Travelin'!!