Supermarket-wise I'm only familiar with MT Supermarket, but they are huge and I used to shop there fairly regularly when I worked in the area:
MT Supermarket | Contact Us
They are way north of campus, though, so I'm not sure what your transportation situation will be like.
I honestly don't have much to say about the restaurants around campus - my experience is limited and what I have had I haven't been impressed with. I'd hate to give you recs for places too far outside your travel area, but if you think you'll be venturing out around town, PM me and I'd be happy to share my faves as well as some of the places I'd try to avoid. I've VERY picky about my Asian food so I'm the same as you when someone recommends an Americanized restaurant like PF Chang's, etc. I haven't been terribly impressed with the cuisine in Austin (I grew up in Nor Cal and I know my way around Chinatown in SF better than I probably do my hometown lol) but there are some diamonds in the ruff. There is a lot of great food in Austin, not just Asian, but man is there some crap, too. lol
Dang it, I really hope it's cold tomorrow, because now I'm craving some chicken pho.