Colonia del Sacramento

The Río de la Plata forms Uruguay's southern boundary. It's allegedly a simple matter to cross if you want to want to visit from Buenos Aires. You just get on a ferry.

The nearest town of interest is Colonia del Sacramento, a UNESCO World Heritage Site. I've indicated the route by adding a red line to the ceramic mural map pictured above. Don't be deceived by the short length. A hydrofoil takes an hour to make the crossing, and a normal ferry takes three. Halfway there, no land is visible. The horizon is water in any direction.
(Incidentally, your atlas probably identifies this as the River Plate, because that's what the British called it long ago. Someone told me the English misunderstood the Spanish word plata to mean "plate", but I don't think so. They knew perfectly well the river was thought to be an artery into South America's silver country. An old meaning of "plate" is "silver", hence "the Silver River".)
Colonia, so called by locals, is the oldest city in Uruguay. Founded in 1680 by the Portuguese, it changed hands frequently, from Portugal to Spain and back, then likewise from Brazil to Argentina and back, not settling down until Uruguay became an independent country in 1828.
Here we relaxed away from the noise and tumult of BsAs in a quiet, tree-lined place, surprisingly free of tourist crowds.

A ferny town wall, with gate and drawbridge, offered ineffective protection during many sieges.

An old iron cannon mounted on a beautifully preserved gun carriage still defends the historical quarter.

Old walls make beautiful subjects for a photographer.

An abandoned building serves as canvas for a religious mural.

We did run into a few tourists. Here, four young Porteños pose atop a cannon in front of the city museum.

Do they fit the category of Beautiful Men?
The water here is said to be clean enough for bathing, probably a good thing as in summer, it gets hot. On the day we visited, the high temperature exceeded 100º. Jean and I wilted in our city clothes. The four young Porteños stripped down to their boxers and cooled off in the river.

A small yacht club berths primarily sailboats. The usually smooth Río de la Plata looks like it makes for excellent sailing.

The yacht club restaurant, recommended as the best in town, served shrimp stuffed with gruyère cheese, rolled in cocoanut flavored rice crispies and deep fried. A monumental culinary effort and one that failed.
Souvenir shops, galleries and restaurants occupy many colonial buildings, like they do in San Miguel de Allende. A block or two from the commercial district, lovely homes doze among old trees. I particularly admired this one. It's not for sale.

But this one is.

It's a huge stone waterfront house. It was much too hot to chase down the realtor, but I doubt it's priced over a million dollars—maybe much less. In Malibu, it would cost thirty.
The town has a functioning lighthouse. The Río de la Plata is a major shipping channel, and there's not a lot of room for navigation error, compared with the open sea.

In front of the lighthouse are the ruins of the 17th century Convento de San Francisco.

But nothing much happens in Colonia, and it's hard to travel to anyplace else. So you need to be looking for rest and relaxation primarily, if you're going to settle here.