Like out shopping or eating or walking through the city, whatever. I've noticed if I leave campus, out in public girls really keep their eyes to themselves. I don't know if it is fear of men or if I'm just ugly/average looking..
If the guy is cute and I catch him looking I'll stare right back for at least 3 seconds (really 3 mississippi's is a long time when you're a shy girl) then look down quickly with a shy smile. After that I may attempt some quick afterward peeks.
If the guy is creepy and or giving off some bad vibes I will peek just enough to keep a healthy distance between him and i.
If the guy doesn't do anything or whatever to warrent attention tho I will look just to see, then go about my business.
I don't care who you are or what you look like, I always smile! Haha, maybe I'm weird, but I even think it's cute if an old couple's walking their dog or something and they smile and nod at you. Smiling at strangers is kinda dying out with people in my age group though, wish I knew why : )
I avoid eye contact with people because I feel like people think I'm staring at them or something. Wearing big sunglasses helps because people don't really know where I'm looking but generally I avoid eye contact with people I don't know
i avoid it with most guys(especially the hot ones...unless they look first and smile or say hi) but its only because you never know what kind of glance you will recieve back. the guy might look at you like you are an idiot, or frown up and even though you know you will probably never see that person again that scares your ego for a while.lol.
and then if it's a reaally cute guy, I'll watch him out of my peripheral vision (so he doesn't know I'm looking at him) when I walk past him, that way he can look at me without us making AWKWARD eye contact.
Personally I'm pretty comfortable making eye contact with anybody for any reason. I work with the public, so I have to. The only time I really avoid a man's gaze is when he's blatantly checking me out and making me uncomfortable (aka: he's creepy), or when he's really good looking and I'm blushing at the thoughts I'm having (hence the slightly embarrassed glance away/downward etc.)