Yes, keep the article. It belongs to the name.
Like The Hague.

Yes. The article is part of the name, and therefore I think should be kept as it is

Keep it as is!!

La Rioja (Spain) - Wikipedia, the free encyclopedia
History|Geography|Economy|Transports and commerce
La Rioja is a province and autonomous community of northern Spain. Its capital is Logroño. Other cities and towns in the province include Calahorra, Arnedo, Alfaro, Haro, Santo Domingo de la Calzada, and Nájera.
en.wikipedia.org/wiki/La_Rioja_(Spain) - 75k - Cached

La Rioja travel guide - Wikitravel
Open source travel guide to La Rioja, featuring up-to-date information on ... La Rioja (Spain) From Wikitravel. Europe : Iberia : Spain : Basque Country and ...wikitravel.org/en/La_Rioja_(Spain) - Cached
Guide to La Rioja, Spain
La Rioja is both a province and an autonomous region located in the North of Spain. ... La Rioja's main economy is wine production and its related industries (wine ...www.euroresidentes.com/euroresiuk/guides-spain/guide-to-rio... - 68k - Cached
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Map of La Rioja Wine Region in Spain. ... La Rioja Wine Tours Weekend. San Sebastian Wine Tours Weekend. Seville Wine Tours Weekend ...www.cellartours.com/spain/spanish-wine-maps/la-rioja.html - Cached
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VIP private wine tasting tour of La Rioja that include your own chauffeur, accommodation at luxurious wine hotel and ... La Rioja is without a doubt Spain's ...www.cellartours.com/spain/wine-tours/luxury-la-rioja-weeken... - Cached
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... to your mind when you listen La Rioja is probably the wine bearing the ... La Rioja offers great possibilities for rural tourism, and if you like hunting, ...www.red2000.com/spain/region/r-rioja.html - Cached
Rioja (wine) - Wikipedia, the free encyclopedia
History|Geography and...|Wine regions|Viticulture...
Rioja is a wine, with Denominación de Origen Calificada named after La Rioja, in Spain. Rioja is made from grapes grown not only in the Autonomous Community of La Rioja, but also in parts of Navarre and the Basque province of...
en.wikipedia.org/wiki/Rioja_wine - 74k - Cached

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La Rioja is a region in Spain and you should preserve the name in Spanish as a proper name. The article is part of the name and it should appear as such.

My undertanding is that the name of the geopolitical unit is, in fact, La Rioja. This is not unique to this specific case, as it also happens with "The Netherlands" (you can call it Holland, but not simply Netherlands" [Los Paises Bajos?]) and The Hague.

I would leave it "untranslated".

I think this should be clear to everyone. Some mini-nationalists might object to the use of the word 'regional' but as this is for foreign consumption it should be okay.