Hi,
the better way to visit places is to ask people that live there. I don't know if is considered spam or advertising but I suggest you to check out this site:
CouchSurfing
is a "community of travellers". You can ask to be hosted free by people in their places or just ask them to show you the city, or just get out for a coffe. It's a great community and people are very easy going and fun.
For the flights, I really don't know from America to Europe, but once in europe if you want to move from spain to italy or italy to spain I suggest you ryanair. Is cheap. And for some period they have special price and you can get a two-way ticket for about 40€.
Hope it helps,
Bye