July 3 to July 9 in Switzerland

My only thought is about the last day - you will be travelling for 6.5 hours, plus connecting time.
When you get to Bergamo you will have more travelling time if you are staying in the upper town.
Where are you going after Bergamo?

Yes, we took this into account and booked two nights in Bergamo. This gives us a full day in Bergamo without it feeling rushed and also the flexibility for us to rest the night we get there if we feel tired.

I was going to post the Italy leg separately but since the question was asked I can post the Italy leg here including the July 9 travel day.

July 9 — Wengen → Bergamo

🏨 Bergamo (Night 1)

Transit

• Wengen → Interlaken Ost (~25 min)
• Interlaken Ost → Lucerne (~1 hr 50 min)
• Lucerne → Arth-Goldau (~30 min)

Booked Train

EC19

• Arth-Goldau 12:18
• Milano Centrale 14:50
• Duration: 2 hr 32 min

Then:

• Milano Centrale → Bergamo (~50 min)

Evening:

• Città Alta

⸻

July 10 — Bergamo

🏨 Bergamo (Night 2)

• Città Alta
• Piazza Vecchia
• Funicular
• Relaxed day

⸻

July 11 — Bergamo → Sirmione → Bardolino

🏨 Bardolino (Night 1)

Transit

• Bergamo → Sirmione (~1 hr 30 min)
• Sirmione → Bardolino (~45 min)

Activities

• Scaliger Castle
• Old Town
• Gelato
• Lakeside lunch

⸻

July 12 — Lake Garda Relaxation

🏨 Bardolino (Night 2)

• Swimming
• Ferry rides
• Relaxation
• Explore Bardolino

⸻

July 13 — Flexible Lake Garda Day

🏨 Bardolino (Night 3)

Choose based on weather:

Option A

Lazise
(~15 min)

Option B

Malcesine
(~1 hr)

Option C

Riva del Garda
(~1 hr 30 min)

Option D

Another swimming/relaxation day

⸻

July 14 — Lake Garda → Venice

🏨 Venice (Night 1)

Morning

• Final swim
• Relaxing breakfast
• Lunch by the lake

Transit

• Bardolino → Peschiera del Garda railway station (~25 min)

Booked Train

Frecciarossa 9731

• Peschiera 14:44
• Venezia Santa Lucia railway station 16:10
• Duration: 1 hr 26 min

Evening:

• Grand Canal stroll
• Dinner near San Marco

⸻

July 15 — Venice Highlights

🏨 Venice (Night 2)

• St. Mark’s Basilica
• Doge’s Palace
• Rialto Bridge
• Gelato and wandering

⸻

July 16 — Murano & Burano

🏨 Venice (Night 3)

Transit

• Venice → Murano (~20 min)
• Murano → Burano (~30 min)
• Burano → Venice (~45 min)

⸻

July 17 — Fly Home

Transit

• Venice → Airport (~30–45 min)

July 5 looks awkward to me. Long way rather out-of-your-way to see a waterfall. It is beautiful, but you have so many other beautiful places you could see with your time.

If you decide to do it, store your luggage in Interlaken and return there via boat to retrieve it. It is about 2 hours from Hotel Geissbach to Wengen, BTW.

Alternative ideas:

• get to Wengen as early as possible and do your July 8 activities
• settle in Wengen and go down to Lauterbrunnen for the afternoon, walk to Staubbach Falls or even walk the whole valley to Stechelberg.
• Another Lauterbrunnen based idea, Consider riding up to Grütschalp and walking to Mürren, an easy walk with terrific views. Return by taking the cableway down to Stechelberg, bus to Lauterbrunnen and train to Wengen
• Check your luggage in Interlaken and go up to Harder Kulm before proceeding to Wengen, also on a historic funicular

You might benefit from the Berner Oberland Regional Pass along with the HFC.