Looking for local designer brand in Roma or Venice

Thank you for much for ur great support in advance. Is there anyone knows well about Italy or European brands? I’m supposed to go to northern Italy, Venice, Siena, Florence and Rome in this March for 7days trip. Unfortunately I’ll join in tours since this trip to Italy is my hubby’s very first trip abroad, and for short limited free time in VENICE and ROME during the trip, I’d like to buy leather bags(if possible made in Italy) for our remembrance. By goggling websites I only found the info of high branded bags that I can buy anywhere like PRADA, GUCCI, not so special to me. Local designer bag like COCCINELLE is preferable ( or European local brands that mainly have launches and distribute in Europe)

Do you have any ideas about affordable local brands (clothing brand would be okay too, they’ll handle with bags too, perhaps)

Highly appreciated if you can give me details, Brand name, locations, or any other roadside stores, whatever you recommend.