I can't speak directly to Washington School, but we were in a similar position looking for schools a few years back and we ended up living in Belgrano R and sending our child to Belgrano Day School. If I had to do it again, I would live in the same neighborhood with the same school. There is a direct train that takes you to Retiro in about 15 minutes, and if you walk 8 blocks or so to Cabildo and Juramento, you can catch the subway. Plaza Castelli is a great park for kids, and the area in general is very mellow, but there are still great restaurants, cafes, etc with a city buzz. It's a nice option to live in the city without moving out of Capital to the northern suburbs. I do like Palermo, but Belgrano is perfect once you have kids. Also, it was kind of cool that there were virtually no foreigners and tourists, so shop owners and neighbors were really friendly and interested in meeting us and finding out why we were living there. The only difficult part was finding an available apartment, because people never move! Also, everyone at Belgrano Day School was super responsive to the particular needs of our family, and we were really happy with the quality of the education.
Do remember that school in Argentina starts in late Feb or early March, so your kids would be coming in midyear. We chose to move at the beginning of the Argentine school year (and pull our child out midyear at home), and I think that made the adjustment easier. If you have a choice of timing, it's something to consider.
Best of luck!
