Do you know of traditional hotels in buenos aires?

honeymoon
on a budget

Argentina`s peso has a very convenient exchange rate to the dollar and euro, that will help, specially with meals and ground travel!!!
As for hotels, you get the usual run of 5 star hotels at international fares and smaller, "boutique" ones. I suggest you search the Internet, knowing that Buenos Aires city can be divided into the following tourist districts:
Puerto Madero: Trendy and expensive, river-side, lots of restaurants and next to downtown.
Downtown: Lots of movement during the week, and empty on weekends. Not too nice if on a honeymoon.
San Telmo: Something like "old town", next to downtown and with lots of fellow tourists around.
Recoleta: Fashionable and classic, the nicest place to set as home-base.
Palermo viejo: This district is just beginning to show its potential, you麓ll very likely find good deals. You'll probably find yourself a bit far away from the fun.
Enjoy!!!

hotel del ritz

I don't know ... but this is my point of view of the city ...

Puerto madero is nice but it has no charming yet and you're not gonna find any budget here
Recoleta is the best neighbouhood in the city where the upper middle class live but it's becoming too touristy
So my advise is to stay in Palermo neighbourhood, you will find here the best nightlife, full of restaurants and bars of any kind

good luck