Strangely Approaching Strangers

Do you ever walk by a group of people that you just want to run up to and ask their name and to be friends? No? Well I do. Every. Single. Day.
Being in Florence, the tourists come in like bees surrounding honey in a hive. There are new students studying here, students visiting, and the typical tourists coming to see the infamous Duomo and carry around a huge map pretending to know where they're going when really, they are completely lost.
Right now in Florence there are over 4000 American students staying for school, including myself. There are days when I walk by myself and I see a huge group of people gathering in a piazza to go somewhere or just to meet up. Even if they're Italian or American, I want to approach so many of them. There are groups of guys that will just look over at me and my friends and we're just not sure what to do or how to respond. Should we go over there? Should we be creeped out? I mean, most of these groups are our age and here for the same reason. I feel like if I do approach them, one of two things will happen:
1. They will start a conversation and we will hopefully hang out and be glad we met.
2. They will be so creeped out by us that walk away and leave you standing there in shame.

Obviously, you would want the first one, but I think the fear of the second one happening is what prevents us from approaching random kids on the street. I think one day I will approach one of those groups of guys and pray that the first option occurs. If not, at least I know that I tried and can say that I did try to attempt to be more outside my box when it comes to socializing.