Although I think a person should say hello when they see someone that they know, I find absolutely nothing wrong with avoiding a shopping center or grocery store during busy times. Nor do I find anything wrong with going to a place where you don't know anyone.
I think everyone has a right to their privacy that way. It makes things easier and more peaceful sometimes.
But, there is something to be said with making friends and building a network of support in your town or community by letting people get to know you. Of course, there will always be jerks that you have to navigate through, but the rewards of making contact with people in a positive way probably outweigh that. I feel like a hypocrite because this part is hard for me personally...due to past experiences...but this has nothing to do with you.