Joe
Uruguay has best beaches than Argentina. Fact. The sediments of the Rio de la Plata come to Argentina making clearer waters in Uruguay. So I would chose always over Argentina.
Punta del Este is VERY expensive. Dollars expensive. Think in dollars. 1 dollar = 15 pesos arg. I suggest you go to other beaches in Uruguay, less fancy, but equally good IMO. You can go, from Punta, to the East (Rocha) or to the West (Costa dorada). Both are more expensive than Argentina, clearly, but cheaper than Punta.
Rocha is a destination for young people, middle class hippies argentines in their twenties. Music, Marihuana, etc. You even have one town without electricity, with almost no comfort practically. Except for La Pedrera, full of elderly people, but it is too small, you ll probably get bored there in a week. You can make Rocha more bourgeois style, there are nice cabins to rent, beautiful fisher towns. You ll need a car though, to go from town to town. Aguas Dulces, La Paloma, La Pedrera, Valizas, Punta del Diablo, Cabo Polonio, Castillos, etc, those are the little towns, some of them pintoresque, of Rocha. Theres not very much infraestructure. 70% of that area is based on the beach. Beach is everything. On a rainy day theres pretty much nothing to do. But eat churros.
If you go to Costa Dorada, it is cheaper than Rocha, "beach towns" like La Floresta, Belo Horizonte, Mar Azul, and then you have nice cities like Piriapolis or Atlantida. You wont be needing a car but public transport isnt good in all Uruguay. I mean urban transport isnt good. What it is good is the "interdepartamental" buses from MVD to the coast every 15 minutes in summer. And relatively cheap. That beaches of costa dorada are nice, there are days when the water is brown, because is still river, but its ok. It is very quiet, you must know, like all Uruguay, if you are a person who needs movement you ll get bored easily.
I think Montevideo is what are you looking for. Beaches, lots to do, as is the most important place of Uruguay, lots to travel, walk around, no car needed and cheaper than the coast. I dont know really of places where you can stay, try gallito luis inmuebles also useful for Punta, but you have pensiones and two or three stars hotels. I dont think rentals for a month are available. Surely cheaper than Punta. Public transport is better than other places (though not like Baires). Montevideo is a very nice city, beautiful architecture, very quiet, quiet people, slower pace than BsAs of course, better food quality. Fruits and vegetables are far tasty in Uruguay than in Argentina. The same with coffe and meat, for example. But is expensive. Plus, you can go whenever you want to Punta, for 5 days or whatever you like. Transport between Punta and MVD is cheap.
Some useful links:
http://www.gallito.com.uy/inmuebles
http://www.casaseneleste.com/
http://www.apuntavamos.com/apartamentos_alquiler.asp
It is very difficult to find something for a month for U$S 1000. I looked and prices are pretty much the double.
If you decide to go to Punta, keep in mind, that you will certainly need a car, just to know the places, beaches, etc, Punta is not a town, is a "band" city, an extended, "edge" city, which goes for 100 kms from one tip to another. There are lots of different places to go, beaches, barrios, etc. From Jose Ignacio to Punta Ballena.