One of the travails of moving to a new community is learning all over again the things that are second-hand in your old one. You know where things are - you know where the grocery store is (and what it's called) and where the dry cleaners is and all those sorts of things. When you move to a new place, all of that is new and sometimes a little scary.
I've even read on forums people complaining because there's not enough grocery stores in Austin, Texas, not enough variety! Well, that's clearly nonsense, but they are new to the area and they probably haven't taken the time to drive around to find the numerous alternatives.
To make it easier for those of you moving here, I'm going to give some hints as to the best places to buy groceries. Not all of them - that would take too long and would take all of the adventure out of it - but enough to get you started and keep you fed while you get your bearings.
First, there's H.E.B. (named for the founder, Howard E. Butt, and it's pronounced H - E - B). It's a Texas chain, and one of the larger chains in our area. There are several different kinds of HEBs, from the rather ordinary super market through upscale supermarkets with wine stewards to the crown jewel, Central Market. As a confirmed foodie, I initially had a very hard time shopping at Central Market without coming out with a few hundred dollars worth of things that I absolutely could not live without and had not known existed until I'd entered the doors - now I've got the swing of it and can actually go in and only buy one or two things that I can't live without and didn't know existed. The Central Market on North Lamar has a cafe that is a gathering place for friends and groups and Meetups, and both Central Markets in Austin have live music in the cafe. Plus cooking lessons.
You could shop only at H.E.B. and feed yourself and your family just fine, and you'll find them all over Central Texas. But there's more options!

Another supermarket that is found throughout our area is Randall's. Similar to H.E.B., Randall's used to be a bit more expensive, but recently they lowered prices dramatically and are more in line. I can find some things at Randall's that I can't at H.E.B., and vice versa. (The Randall's at William Cannon and Mopac, however, has really good chocolate chip cookies in their bakery, just in case you're interested.)

Brookshire Brothers is another Texas chain. They're found more in the small towns surrounding Austin, and while they're usually smaller stores, a really nice one has recently opened in Salado - was there just today picking up the makings for a marinara sauce, and noticed a very nice and unusual selection of wines among other things. I'll be going to that one a lot more often, I think.

Crestview Minimax has been serving Austinites since 1953. Located in the hot Crestview area of Austin, it's an old-time neighborhood grocery.

Most of the small towns around Austin have their own local grocery stores, like the Jarrell Supermarket. (And most of those local grocery stores don't have websites, because everyone who lives there knows everything they need to know about them already.) As Jarrell has grown, so has the store's offerings, and it's a great place to shop or pick up a pizza and a movie without having to drive into Georgetown or Salado. You can find something similar in most of the small towns, if you should be on a day trip and suddenly need to drop into a grocery store or, of course, if you move to one of those small towns.
Another small chain that's been around Austin for a while is Fresh Plus. There are a few sprinkled around town (Clarksville, Hyde Park, etc.), and while a little pricey, they're a good neighborhood grocery.
Another blog will cover the health and organic food stores around the area, from the Whole Foods flag ship store on 6th Street (you did know that Whole Foods was born in Austin in a tiny building on 5th Street, right?) on down. We've just scratched the surface of places in Austin to buy food.
I am a big HEB fan! I actually liked Randalls better before Safeway bought them but they are okay also. We don't have Crestview though.