If you want to reach the highest tips of the Alps you must go to Italy (although the location of the highest cliff of Mount Blanc is still an open controversy between Italy and France): Mont Blanc, Matterhorn and the Pink Mount are all in Italy, (although they are accessible also from France and Swizterland)
One thing that most of the visitors often take for granted is that Italy has always been one single Country. The truth is pretty different. I think it might be useful to offer you with another perspective and suggest a different travel itinerary based on the process which led the Italian Peninsula to unify itself under the flag of a single Monarch: the House of Savoy.
Torino is a blessed city. Most of the conteporary architectures are well inserted within the city context and allow keeping the original elegance by also experimenting contemporary and innovative architecture.
I choose to overnight in Taormina as I had planned an excursion to the summit crater of the Etna Volcano the next morning. Taormina is a perfect gate to the Etna, although you may also start from Aci Reale or Catania as distance is pretty much the same.