I don't think the FS or Alvear Palace are up to snuff. PH is a nice property, but very expensive as you mentioned.

I really loved the tiny Relais & Chateaux affliated property called Algodon Mansion. IMHO it has among the best hard product in the city and the staff are really trying to get up to 5-star level. It is pricey much like the rest, but this hotel really feels more like a private luxury home than a big hotel.

BA is also known for its funky and occasionally luxurious boutique hotels. You are certain to find one that fits your style and amenity needs at any price point.