Buenos Aires is only separated from Uruguay by the river Rio de la Plata. The fastest and easiest way to get to Uruguay is by ferry. Either with Buquebus or ColoniaExpress. Buequebus has its port in the northern part of Puerto Madera, ColoniaExpress in the southern.
The cities in Uruguay that are suitable for a short trip are Colonia del Sacramento (only 1h by ferry), the capital Montevideo (only just over 2h by direct ferry with Buquebus, or a little longer by ferry to Colonia + bus). Punta del Este on the Atlantic coast is also a popular destination. This is the city for beach holidays, but is only worthwhile from 3 days. Otherwise the way to Punta del Este is too long.
Colonia del Sacramento is the nearest town. With the ferry from Buenos Aires you will start. Tickets can be bought online. At the ferry terminal you have to go to the check-in, no matter if you wanted to check in your luggage or not. Then you have to go through the security control similar to the airport. Afterwards to the passport control, but with the small difference that you get your entry stamp for Uruguay directly in Buenos Aires. on the return trip in Colonia already the stamp for Argentina. This makes the exit much faster, but your baggage in the destination country will still be briefly checked by the customs control.
Colonia del Sacramento is a small towns with great small alleys in the southwestern part. Many nice photo motives with little bushes and sometimes old cars in the streets. The place would be perfect for a photo shooting. There is also a lighthouse from which you have a nice view. For the beautiful city center you need maximum 2h, to see everything. There is also the possibility to go further north, about 5km away, to see the Colonia letters and an old bullring.
Otherwise you have the possibility to spend some time on the beach. The beach has a coastline of about 5km. The beach itself is quite nice, but you are not at the sea but at the river. Even if the river is so wide that you can only see water on the horizon, it remains a brown broth. Colonia is a good day trip. I had an overnight stay, because there was not enough time for Punta del Este, but I still wanted to do a beach day.