a couple of options.

See this:

http://www.frozenfoodage.com/web/online/NEWS/Small-Store-For...$1099

and this from Wikipedia:
"Tesco Express

Tesco Express stores are neighbourhood convenience shops, stocking mainly food with an emphasis on higher-margin products (due to lack of economies of scale) alongside everyday essentials. They are found in busy city centre districts, small shopping precincts in residential areas, small towns and on Esso petrol station forecourts. There were 827 stores at 23 February 2008 year end, with a typical size of 190 m² (2,100 sq ft).[citation n"

Hi SpanTran,

If you're not too sure about "local supermarkets", maybe neighbourhood/neighborhood supermarkets will do the trick.

Good luck!

Álvaro :O)


Tesco | Business | guardian.co.uk - [ Traducir esta página ]Tesco today continued to extend its international reach, announcing plans to buy a struggling neighbourhood supermarket chain in Tokyo. ...
www.guardian.co.uk/business/tesco?page=33 - 91k - En caché - Páginas similares
foodanddrink-market-foundations - [ Traducir esta página ]The stock on the shelves certainly appeared to be a cut above that available at the average neighbourhood supermarket, such as a Sainsbury’s Local or Tesco ...
www.thecnj.co.uk/review/2008/041008/foodanddrink041008_02.h... -

Small centrally located store featuring ease of access, late-night hours, and a limited line of merchandise designed for the convenience shopper. Convenience stores charge above-average prices compared to large supermarkets that generate large-volume sales.

may be another option, at least in the US. They're usually part of gas stations.

My answer is from a UK perspective:

Firstly, I think it is important to maintain the word 'supermarket' in the translation'.

local supermarket is fine but it could mean two different things: a supermarket that is nearby in proximity or a supermarket that is smaller than a large supermarket to serve a local area.

-'convenenience store' in the UK could have a connotation of a small local shop / newsagent or of a slightly larger supermarket. So by using 'convenience supermarket' this eliminates the smaller connotation.

- mini supermarket: again widely used in the UK and works well if you consider the definition given in your text.

All the big brands in the UK have their own trademark for refering to this type of things; Tesco Express, Sainsbury's Local, etc.

See the reference below, which uses a variety of the terms and IMO points towards using mini-supermarket in your context
http://www.corporatewatch.org.uk/?lid=2383

Sainsburys Local and Tesco Express are also rapidly replacing neighbourhood convenience stores and corner shops and are appearing on petrol station forecourts; Tesco now has 5% of the convenience store market.[4] Temporarily thwarted in its plans to build out of town retail sheds and rapidly losing market share to Tesco, Asda has recently shifted direction and is also about to enter the convenience store market for the first time, with plans to open discount mini-supermarkets to compete directly with Tesco Metro stores.[5]


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Note added at 1 hr (2008-11-24 14:05:37 GMT)
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Actually on second thoughts, I prefer 'convenience supermarkets' to 'mini supermarkets' because it captures the 'de proximidad' part.

Una alternativa adicional.
¡Suerte!

In Argentina, los supermercados de proximidad were known as minimercados before being given the current name. Perhaps mini market is an option that serves your purpose.

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Note added at 2 hrs (2008-11-24 15:07:53 GMT)
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Los supermercados de proximidad son autoservicio. La clasificación, de mayor a menor, es hipermercado, supermercado y supermercado de proximidad.

my option