Hi, its best to go to Uruguay if you want to play it safe, have some fun, and come back to Argentina, the overstay of your 3 month visa is actually $100.00 USD.. or you can just stay for as long as you need and pay $100.00 USD the day you leave.
If not, you will have to go to Uruguay every 3 months, thing is if they catch you ilegal, deportation will be more expensive and they will fine you with over $3000.00 USD, yet, Argentinean Immigration authorities are not on the look out..
very important, if you do go to URUGUAY, MAKE SURE THEY STAMP YOUR PASSPORT, MANY TIMES THEY WILL JUST LET YOU GO BY WITHOUT ANY STAMPING... Argentinean immigration is in URUGUAY before you get on the the ship to come over here, if you dont get stamped you wont get stamped in Argentina... and viceversa...