I hate being rushed. The only time I can tolerate it is on a Rick Steves tour. So far I've done 5 of them and I've arrived early and stayed late for all, not necessarily only at the tour beginning and end locations.
There are lots of ways to add time before and after RS tours. These are 3 different ways I've done that:
The least time I've traveled in Europe was about 3 weeks in 2018 when I did the RS Best of Scandinavia tour. I spent 2 nights in Stockholm before the tour started and 1 night in Bergen after it ended. That was sandwiched between 3 nights in my European arrival city of Amsterdam and 2 nights there before flying back to the US.
My trips are usually 4-6 weeks long.
In 2017 I sandwiched Village Italy between 6 nights in my arrival city of Rome, 2 nights in Ravenna and 5 nights in Venice before it started, and 3 nights in Milan, my departure city, after it ended. I spent the time in Ravenna because the VI tour only included a brief, enroute-to-somewhere-else, visit and my last time there was in 1977. The extra time in Rome and Venice, staying in apartments in both, was to see and experience things I hadn't done before in those cities. The extra time in Milan was because I'd never been there before.
This summer I was gone about 5 weeks. I did my first back-to-back RS tours, Heart of Portugal and Best of Spain. Based on advice from others on the Forum, I did Portugal first so as to have a few days between the 2 tours. I also used Amsterdam as my first European arrival city and my departure city. I actually stayed in Haarlem 3 nights before flying to Lisbon 2 days before the start of the tour, staying in the tour hotel.
I wanted to stay an extra night in Porto at the end, but they had no rooms available, so I flew to Barcelona the evening of the last day of the Portugal tour. I spent 3 nights there, in the tour hotel, before the start of the Best of Spain tour. I spent 1 night in the Sevilla tour hotel before flying back to Amsterdam where I spent 1 night in a hotel close to the airport before flying back home.