So many options ... what would interest you? I'll stick to transport methods where you don't need rent/drive your own vehicle:

Venice? Verona (traveling in opera season?), or Vicenza; unless the cathedral of St. Anthony at Padua is an attraction. Could go to Trieste via Udine through Friulian foot hills of the Dolomites. Consider day tripping other islands in Venetian lagoon ... Vaporetto to Murano for glass tours followed by Burano/Mazzorbo for lace and color (Michelin star restaurant Venissa if your splurging on lunch/dinner or a very unique local wine \"Dorona\" $$$ produced from grapes grown on the island); consider adding Torcello and you've got a 3-stop trip on public transportation. Back \"home\" for dinner. I've never been to Chioggia but hear it's worth the visit. For me, skip the Lido - it's suburbia Venice style with a beach and casino' - the gambling type, not the other type of Italian casino :-)

LaSpezia? Le Cinque Terre is obviously the big one, Portofino the other. Nice, but anticipate day tripper tourism crowds.

Milan? Up to Lake Como? down into Piemonte wine country - tours galore, \"slow food\" movement started there. Mountain visit in Val d'Aosta. Radical thought ... skip Milano and go to Torino :-) a place less on the tourist trail but interesting nevertheless.

Florence: Sienna piazza and cathedral (will you go when carpets are up and floor mosaics are on display?); wine country excursions - plenty options, duration and price levels; to Lucca for bike ride on the wall; to Pisa for the Tower/Cathedral/Baptistry. San Gimignano is a popular bus trip thing - cute piazza with a few towers left standing, a unique local wine and some interesting shops (colorful pottery art, traditional in the region)

Enjoy!

Looking for day trips by train from Rome, Florence, La Spezia, Milan and Venice