So much depends on where in the Recoleta and in Palermo you choose to rent. Palermo has many subsections, ie Palermo SoHo, Hollywood or Viejo...just plain Palermo and Palermo Chico. Palermo Chico in general might be considered the Embassy area with many fine residences and apartments. Also the Palermo Woods are nearby which is a fantastic public park. Palermo SoHo/Hollywood is a bit more bohemian and still undergoing gentrification in some areas so you might find a few blocks of one street very upscale and fashionable and then later a bit edgier.
The Recoleta has some really outstanding residential areas and then some that are nice but not as fashionable. Both areas tend to offer many public parks and green spaces and a good selection of super markets (as long as the farmers don't go out on strike again)
As for your agent I have no personal experience with them but have heard they are good to deal with, another would be
www.apartmentsba.com so at least you might compare. I assume you know you will be visiting during the later part of winter so be prepared for some chilly weather.
Once you have narrowed your selections down on apartments you might post again with the locations and get more specific feedback on the locations.
suerte
SAM