If you think you have enough money to make a new investment, then do not look for an apartment that is available for rent. Look for apartments up for sale instead!
And when this comes to mind, we have websites like Viviun.com, which provides comprehensive information on apartment units listed around the world, including Uruguay. Most of the units listed are in Montevideo or Punta del Este. See more of them here.
Link: Apartments For Sale in Uruguay - Available Properties - Viviun the Leader in International Property Listings
