You could ask the same of St Tropez. Both were once fishing villages.

It might have something to do with Uruguay having once been an attractive destination for specialised banking on the continent (you know like the sort in Panama where cash arrives by the bin bag full and questions about its provenance tend not to be too searching). And where the cash goes so too do international jet set trash.

There's plenty to see in Uruguay: its capital Montevideo boasts some excellent examples of Spanish-Italian art deco architecture; Punta del Diablo offers miles of unspoilt coastline (like Punta del Este before the bronzed beauties arrived); and, already mentioned, Colonia del Sacramento old town is precious too, even if a little sedate for some.

The op hasn't mentioned how long s/he intends to visit South America for. I'm assuming 2-3 weeks and suggest the following. I wouldn't ordinarily recommend Brazil for a first timer - that's not to suggest there's anything wrong with it, there's just so much else on the continent I'd place higher on my to do list. Air travel within South America can be costly, so it's sensible to invest in a OW Visit South America air pass.

Day 1: Fly LHREZE.
Days 2 & 3: Explore Buenos Aires.
Day 4: Fly AEPBRC (Buenos Aires domestic airport to Bariloche). Fly down to Argentinian Patagonia, explore the lakes - walk, eat, fish (if so inclined). Stunning scenery. If you can afford it, stay at the Llao Llao.
Day 6: Fly Back to Buenos Aires, take a fast boat across the Plate to Colonia del Sacramento and stay the night. Conveniently, the domestic airport is just across from the port.
Day 7: Return to Buenos Aires, fly AEPIGR (Buenos Aires to Iguazu, Argentinian side). Connoisseurs will tell you to see the falls from the Brazilian side but for a first timer this will be sufficient. Stay overnight.
Day 8: Fly IGRAEPSCL. A bit of a long trip, two flights. The most straightforward way to do this is to fly LA back to AEP and then pick up a connecting flight to Chile on AR. On the upside you won't have to schlep out to the international airport. If you want to stick to flying LA, then allow time for transferring from the domestic to international airports - about an hour on top of your minimum check in time). I'm a big fan of Santiago but as a South America newbie you'll want to prioritise your time otherwise. Stay a night at the Hyatt and ask for a room facing the Andes. Book a table for dinner at Astrid y Gaston - traditional Peruvian food with a contemporary twist.
Day 9: Fly SCLCJC (Santiago to Calama). You're heading north for the lunar landscape of the Atacama Desert. Plenty of pleasant and affordable places to stay in San Pedro de Atacama. Hire a car so you can go off to explore the lagunas and (although the hire car company will tell you it can't be done without a special permit) neighboring Bolivia. Tip: don't stop at the border, if you're driving a rental car.
Day 12: Back to Buenos Aires via SCL. Stay one night in Buenos Aires - the Alvear Palace (picture the Paris or London Ritz transposed to South America) is a fitting swansong.
Day 13: Fly back to London.
Day 14: Arrive London.

If you can tag on an extra week or two some further suggestions:

- Easter Island: magical and has to be visited once in a lifetime. 2-3 days is sufficient to 'do' the Island. Flights are only to/from SCL.
- Around 3 hours' drive from Santiago: Valparaiso. Chile's capital until the Panama canal was started. UNESCO World Heritage site.
- Chile's south: Volcanoes and lakes, further south the awesome Torres del Paine National Park.
- Peru: head straight for Cusco and onwards to Machu Picchu. If you have time to stop for a meal in Lima, the city is emerging as a formidable contender in cuisine. Most of the better restaurants are in the upscale Miraflores district.

If you are intent on exploring Brazil, given the pricing structure of flights within South America, bear in mind it'll be cheaper to buy travel within the continent ex Argentina than ex-Brazil. My suggestion is that Brazil is a complete trip in its own right. But to your earlier question: San Paolo v. Rio, no contest. The latter for its sheer beauty.

Enjoy!