1. Argentinan beaches in August?? noooo way. same goes for uruguayan ones...hello?? winter???
2. If you're going to be staying till it gets warm..."nice" argie beaches Villagesel, Pinamar. In Uruguay Punta del Este (if you happen to be a Millionaire...) Valisses, Punta del Diablo (cheaper, still not cheap though; Uruguay is expensive).
3. What's wrong with argentinian spanish? The accent is strong yes, so? Full of modismos? so is every other spanish! and EVERY country except for Chile claims to have the "purest" spanish. you hear that EVERYWHERE, so who cares whether you learn it with a heavy porteño accent and the "sos" and the "vos"? all that implies, if you learn well that is, is that people will say to you "ah, you learnt your spanish in Argentina"
4. being a foreigner you'll be veeeeeeeeery lucky if you find a room in a shared appartment in a safe/centric neighbourhood for that much money.
hope i was helpfull ^^