Mission shoes are probably one of the most difficult things to shop for. You'll want something stylish, yet you'll also want something that lasts. I remember thinking, "I'll figure it out when I get there." So, here is what I figured out:
1) Not all the shoes you buy will last your entire mission.
No matter what brand or style, your everyday shoes will probably start to give out around 9-12 months; if they do last, they will most likely show wear and tear. The longevity of your shoes depends on where you serve - some islands have rougher terrain than others. I knew very few sisters whose shoes lasted them.
So, while mission shopping, here are a few things to consider. First, look at the sister missionary clothing guidelines (http://missionary.lds.org/dress-grooming/sister/dress/shoes/?lang=eng). The shoes listed under Everyday (and the 3rd picture under Flats) are shoes that will probably last you into the year mark range. Flats can also last, depending on how much you wear them. Second, consider buying shoes that are black or brown. They can be polished, which will increase the life of them. Third (this probably only happened to me), you can buy new in-soles for your shoes if the original ones gives out. Fourth, well-known brands won't necessarily last you longer, though they often will. For example, I had two different pairs of Naturalizer's - one I purchased while preparing and the second while I was serving. The first pair (which looked more like the Everyday shoes) lasted me my entire mission (though I had to replace the in-soles). The second pair (which had a sole like this) lasted me about 4 months before the finishing started wearing off. I had a companion that had a nice pair of Clark's sandals - they lasted her 14 months before the strap on one ripped. Beyond the broken strap, the shoes still looked good.
2) If you need to buy shoes while serving:
Island-to-island shoe shopping varies. Grenada and St. Lucia (and most likely St. Vincent) usually don't have women's shoes that will last - if they do, you have to search. I think I saw Hush Puppies in Grenada, but the styles weren't ones that would work with day-to-day walking.
Barbados, St. Maarten, and Trinidad (and most likely Tobago) have standard brands. Cave Shepherd in Barbados has high quality shoes; there is also a store in St. Philip (by the Emerald City grocery store) that sells Naturalizers and other recognized brands. Barbados and Trinidad have Payless (I bought some American Eagle brand shoes from there and they lasted me my last six months, and they're still wearable). Trinidad also has a store in a mall that sells Clark's.
Sisters have recommended the following brands as ones they saw last: Clark's, Naturalizer, Sketchers, and Champion.