Is your town that small that it would be off for him to be there?
I always try to say hello. especially if the split was mutual, and we can both stay friendly.
If it's someone that things are a little bit messy, I would still probably at least say Hi, and acknowledge them. Otherwise I think it would make me look as if I'm still sweating it.
Unless of course if I felt like things with this person were so ugly that the best thing to do would be to simply ignore them.
I guess it really depends on the situation and the person.

It's not a town, but a village, so yes it is small.
And we didn't split with huge argument, although I got hurt really bad.
But in a way there's nothing left to say and considering what we had and what happened in the end it is just awkward.
I decided to just ignore him. Not out of spite or anger or anything. Just that I have nothing to say to him. He didn't say anything either, which if he had really wanted, could've done too.

Maybe you find it awkward because at one time you two had a good relationship and all. Maybe a part of you still misses that. IDK. I know I miss the good times in many of my relationships, even though the people I have nothing for anymore, they are nothing more to me now than any other random stranger that passes by in my day to day life, but I miss the good times, not that I'm not over the relationships or anything, but I think it's normal to miss the good things even when we're over them.