If you don't like the perfumes, at SMN you can buy stuff like the great Carta d'Armenia (benzoin perfumed strips of paper), bath oils (eg melograno), or similar body products. You can also stop by the equally characteristic farmacia Santissima Annunziatahttp://www.farmaciassannunziata1561.it/
just south of the said square. Their scents are heavier than the more sedate SMN, though more expensive. The patchouli indonesiano is a blast. They also sell great creams - I like their face and their hand creams for men, they smell very nice.
But probably my best recommendation is to stop at L'O profumohttp://www.loprofumo.com/
a 15min walk west of duomo (there are some very characteristic restaurants nearby, by the way, like la pentola dell'oro). It's a very good niche store, but the lady also prepares perfumes herself. I especially like her Kalos, which is based on (true) ambergris. This year's new offers were two realistic chocolate scents - which are excellent if you like to wear said material (I don't).