Thank you all for the responses!
It' fascinating seeing how dissimilarly people from different cultures can perceive the same name. Also some of the answers were very amusing. 
I should clarify that I'm not looking for a name for a baby, but I am planning to change mine.
I am Italian and while I'd like a name from my culture, I would also prefer something a bit international. My current name is one of those that start with "Gi" and it gets misspelled all the time by non-Italians. It is not the main reason why I'm changing it, but getting rid of that would be an added bonus.
My first choice would be Livia, but Olivia is gaining more and more popularity all over Europe, Italy included, and I'm afraid I'll get sick of hearing it everywhere and regret my choice.
Virginia is a close second, I like the full name but I'm not fond of the nicknames. I hadn't thought of the tobacco association, even though that's what I used to smoke before quitting!
I agree with many posters that Lavinia feels fussy, it's probably considered a bit snob in Italy, which is so unlike me. I put it on my list because it sounds similar to Livia and I could get the nickname Liv from it.
I wasn't expecting Clelia to look made up! I'll take that into consideration.