Let me suggest a couple things. Your general plan is ok...going to another city is a perfectly reasonable thing. And making the mall your first outing is fine to. I believe there is safety in numbers. But before you go, spend some time at the mall en drab and observe what women your age are wearing when they go shopping. You'll see a broad range, but I think you'll find some in nice casual outfits that will work for you. You'll be much more comfortable if you're dressed to blend in. Second, for daytime, consider sandals or slides with a low to moderate heel. There are lots of women who are your height, so that will work well.
