Renting an apartment is one of the more unique qualities of Buenos Aires in that they have an amazingly large range and such an easy process to search and find an apartment in a location you want. No other city can boast of this range or ease of booking. And while inflation is on a tear in Argentina, and food is becoming quite expensive, apartments still are on the reasonable range. Prices for a month's rental range from US$500 to US$2000 for good apartments in good locations.
If staying for a visit of a week of more and you don't need services of hotels, rent a apartment. Very good deals are available, generally cheaper than hotels, but it is a risk that the apartment may not be good, or that there may be some rare case of problems with money - large deposit is required on arrival. But most people have had no problems renting, as can be judged by the number of choices available. ByT Argentina has the largest list of rentals, and they have a large list of mid-priced rentals. They will have an English-speaking person at at the hand-off when you arrive. For what it is worth, I have had good experiences with ByT, but there are many other agencies available.
Note that renting an apartment is far trickier and it is more of an commitment than staying at a hotel. Make sure you ask about everything you need, and check that things like Internet Access, Toilet Paper, Towels, Sheets, Maid-Service, Cable TV, etc, will be what you expect. At one place I stayed, the internet access was listed as available, but did not work for a whole week. And it was not Wi-Fi, but an old USB-based wired DSL with a driver that had to be installed on my computer and which did not behave well and persistently crashed Windows XP on a restart after suspend.
But there is nothing more satisfying than living like a local as much as possible, and for that a apartment rental is the best.