The other place to try is the Barrio Ingles in Caballito. The thing is you are going to have to give up something to get what you want. And I'm not talking about the dishwasher (which I've only seen in extremely high end places or people's permanent homes -- temporary rental apartments tend not to come with them).
I'm with Philip -- outside of major rush hour it can be very quick to get around the city from areas that may appear "far". Perhaps the best I can recommend for you is to rent a place for the first few weeks you arrive and then use that time to get to know other parts of the city that you haven't visited before. The first time you head out to Caballito or Nunez or Belgrano R or wherever it may seem far away, but you'll soon see it's not. EFrom our place we're only a few mins to the Gral Paz as well so it is only about 15-20mins by car (if you go via the city it can easily end up being an hour though). On the subte I have a 5min walk to the station and then 25mins to Obelisco. My sister in law lives in the Barrio Ingles neighbourhood of Caballito and it's about equidistant (timewise) to the centre on the subte.
I'm with Philip -- outside of major rush hour it can be very quick to get around the city from areas that may appear "far". Perhaps the best I can recommend for you is to rent a place for the first few weeks you arrive and then use that time to get to know other parts of the city that you haven't visited before. The first time you head out to Caballito or Nunez or Belgrano R or wherever it may seem far away, but you'll soon see it's not. EFrom our place we're only a few mins to the Gral Paz as well so it is only about 15-20mins by car (if you go via the city it can easily end up being an hour though). On the subte I have a 5min walk to the station and then 25mins to Obelisco. My sister in law lives in the Barrio Ingles neighbourhood of Caballito and it's about equidistant (timewise) to the centre on the subte.