if you see your lover a while after you've broken up, with their new lover, happily going about their day? What's the best way to react? Do you go up to them to say 'hello' or do you try and get away without them seeing you?
I would tell the girl good luck and then walk away haha. I pity anyone who ends up with my ex xD That's just bad news.
I agree that you should just smile at them in acknowledgement, but don't go up to them unless they initiate it because it's awkward (especially if you don't know what your ex said about you). I guess really this depends on how you two broke up in the first place and whether you became friends or enemies after.
I would wave back if they spotted me and waved first, but I would probably try to avoid them. lol I've only been in four relationships my whole life though, and each person pursued me first.