2 -3 week Swiss & Italy trip in Dec 2021

Hi all, this is my first visit to Europe, I plan to visit Switzerland & Italy late next year during Christmas, in December 2021.

I will have about 2-3 weeks, departing from Singapore. I will be travelling with my mother, and we like to take our time to enjoy each location, with shopping and sightseeing. No hiking, as I am afraid my mother can’t take it 🙂

I need help with my itinerary as I am not sure if it is feasible. The plan is to fly into Zurich and depart from Rome. Or vice versa.

I would love to see these following places:

Switzerland: Rhine Falls (not sure if to stay in Schaffhausen? I checked it’s expensive), Lucerne (Chapel bridge, Old Town, Lion Monument, Lake Lucerne), maybe Schlithorn?, Mt Titlis/Pilatus/Rigi, one mountain is enough. I heard Jungfraujoch is expensive and crowded so I am willing to skip it.

Italy: Florence (main attractions), Rome (main attractions – Colosseum, Trevi Fountain, Roman Forum, Spanish Steps, The Vatican)

My Itinerary so far:

Day 1: Flight from Singapore to Zurich (if arrive in afternoon 3pm, relax for the rest of the day, check into Zurich/Schaffhausen hotel? I would like to see Rhine Falls and maybe Old Town around Zurich only. Do I need 2 nights? But I would’nt want to keep changing hotels when I have to carry luggages around.)

Day 2: Zurich (see the Rhine Falls & Old Town)

Day 3: Train from Zurich to Lucerne (around noon, check into Lucerne hotel)

Day 4: Lucerne (explore areas…Chapel Bridge, Lion Monument, Old Town)

Day 5: Lucerne (Mt. Titlis/Mt. Pilatus/Mt. Rigi)

Day 6: Lucerne (Schlitthorn? or free day. maybe one mountain is enough.)

Day 7: Train from Lucerne to Florence (Is there an easier or cheaper route for this where not many stops, and not too long? I just need to get to Venice from Florence, check into Florence hotel. I see some itineraries that go to Venice first from Lucerne, but it is not a place that I’ve dreamt of visiting so I can skip it, unless the route would be much easier.)

Day 8: Florence (Piazzale Michelangelo, Piazza della Signoria, Duomo, Giotto’s Bell Tower, Baptistry)

Day 9: Florence (Galleria dell’Accademia, Basilica di Santa Croce, Ponte Vecchio)

Day 10: Florence (Palazzo Pitti, free day)

Day 11: Train from Florence to Rome (check into Rome hotel)

Day 12: Rome (Colosseum, Aventine Hill, Trastevere)

Day 13: Rome (Trevi Fountain, Ponte Umberto I, Palace of Justice, Castel Sant’Angelo)

Day 14: Rome (Palentine Hill, Spanish Steps, Pantheon, Piazza Del Popolo)

Day 15: Rome (The Vatican Museums, St. Peter’s Basilica, Altar of the Fatherland)

Day 16: Flight from Rome back to Singapore

Overall I think I need:
1/2 nights to see Rhine Falls + Old Town?
4 nights to explore Lucerne + 1/2 mountains?
3/4 nights to explore Florence
5 nights to explore Rome

Any recommendations on decent hotels that are not too expensive? Hopefully under 90 euros per night? Any christmas markets I should be visiting in the areas? Do I have to go to Interlaken to visit Schlitthorn?

Thanks,

Joel