Local as in Phx or Tucson? In Penasco you can pick up cheap umbrellas at the Pharmacia 2000 (or 3000?), Super Ley, the Walmart/Bodega, etc. These are usually under $10, though most places have a couple of different qualities offered. The bad thing about the very thin ones is the shade they provide is limited and barely protect you against any UV rays. If you are stuck with these, we always just throw a wet towel on top of each so as to get a bit more shade. Of course, depending on where the sun is and the angle the umbrella is set at, this is going to either make it extremely stable or something you're constantly tweaking...
In the states, they have a few different kinds at Target ($30ish) that seem to work fine, fabric protects pretty well, plus they have the additional cork-screw-looking white plastic device that will REALLY anchor them well in the sand. The garden dept. in Target has even stronger ones. If THAT doesn't work, I remember seeing a few offered a while back at Ace Hardware, but the problem with all these options in the US is that, for the most part, beach umbrellas are a seasonal item, and a lot of the times these chains will only have a short window of time in which they are available.
