Sharing our itinerary last sep-oct 2015. I used the map to determine our itinerary.

On our planning, we preferred bus over trains since it's a lot cheaper. We use bus for overnight transfers to save on cost plus it became our accommodation already. We use trains for morning transfers to save on time. My husband and I have agreed that this would be a whirlwind type of vacay to cover only our priority/must-visit sites. Bawal magreklamo.
Day 0 [London]: Arrival at night. Roam around Paddington (near EasyHotel).
Day 1 [London]: Viator Tour: Stonehenge, Windsor Castle, Bath and Medieval Village of Lacock
Day 2 [London]: FREE walking Tours (signup online) - London All In One Tour (Change of Guard at Buckingham Palace, photo op at Big Ben and London Eye) and the Dark Side of London Ghost Tour.
Day 3 [London]: DIY: Platform 9 3/4, Picadilly Circus for shopping. Overnight bus (the Roro type) to Paris.
Day 4 [Paris]: FREE walking Tours (signup online) - Paris Landmarks: Right Bank Tour (starts at Opera house) and Montmartre Tour (Moulin Rouge to Sacre Coeur)
Day 5 [Paris]: DIY: Eiffel Tower so early in the morning to avoid crowd, Louvres Museum, Walk the Champs Elysees Street where Arc de Triomphe is, back to see the Eiffel Tower at night (must!)
Day 6 [Paris]: Versailles Palace. Overnight bus to Amsterdam.
Day 7 [Amsterdam]: FREE walking Tours (signup online) - Amsterdam City Tour, did the Heineken Tour and the Red Light District walk
Day 8 [Prague]: Morning flight to Prague via EasyJet. DIY: Prague City Tour (Old Town Square, Charles Bridge to Prague Castle).Overnight bus to Munich.
Day 9 [Munich]: FREE walking Tours (signup online) - Munich City Tour, Viator Tour: Third Reich Tour (Hitler) and HofBrauhaus Beer
Day 10 [Salzburg]: Viator Tour: Salzburg tour (Sound of Music) from Munich
Day 11 [Munich]: Viator Tour: Neuschwanstein Castle Tour (must!)
Day 12 [Zurich]: Early morning bus to Zurich. Pasalubong shopping (Swiss chocs are cheap!). Planned to visit the Rhine Falls, but we decided to skip that.
Day 13 [Interlaken]: Viator Tour: Jungfraujoch Tour/Swiss Alps Tour from Zurich - the only reason we went to Switzerland (must!)
Day 14 [Zurich]: Free tour from Viator: Zurich Tour (Can skip!). Overnight bus to Venice thru Milan.
Day 15 [Venice]: DIY: Venice tour. It's a small city, you can explore in a day. Did not ride the Gondola, it's too expensive. Skipped our planned Burano trip.
Day 16 [Florence]: DIY: Florence tour (Duomo, Piazza della Signoria, Ponte Vecchio, Pitti Palace and Boboli Gardens, Piazzale Michelangelo)
Day 17 [Florence]: Train to Pisa for the Leaning Tower of Pisa then back to Florence for Outlet shopping
Day 18 [Rome]: Early train to Rome. DIY: Rome Tour (Colosseum and the Roman Forum and Palatine Hill, Pantheon, Spanish Steps, Fontana di Trevi (under construction), Piaza Navona)
Day 19 [Vatican]: Viator Tour: Vatican Museum with Sistine Chapel and the St. Peter’s Basilica
Day 20 [Rome]: Our flight is not until the afternoon so we just explored Rome but not the tourist sites until it's time to go to the airport.