Actually I am on the other side of the Cape now in the Garden Route. The city is called Knysna and it's really a nice place. I have a phone that has a 3G connection and I am tethered using the prepaid data plan. It's the first place I have used this type of technology, the portability is great but the connection speed is variable.
Gyms are available with nice lap pools. just keep your $34/month budget for that. Rates can be cheaper if you prepay for 6 longer periods but just leave it budgeted that way and hopefully you can find a better deal. Here is one that I went to for a while, they are very nice:
Red de clubes
Don't even go through the hassle of trying to get a place on contract for 12 months at first. I had a friend from Mexico who had trouble with that and he had lots of local friends. If you want to lower your apartment expense just get a less posh place in a more bohemian neighborhood. San Telmo is a good example of a neighborhood that you can get better prices on places. It's just a little less post then the more high end neighborhoods but has its own feel. You have to be street smart there in all neighborhoods but it's not scary and don't be a fool and walk down an alley at 2:00 am with people following you kind of thing.
Here is a big property management company with a range of places in many neighborhoods:
Reynolds Propiedades Argentina | Página de Inicio
I personally like Las Canitas (next to the polo fields). I found it to be an amazing neighborhood with everything you need in walking distance. The only downside is the subway is not nearby.
As for visa requirements. Just take a day trip to Uruguay. It's very easy and cheap if you take the slow boat. Colonia is a nice little quite town and good for a few hour walk. Then back on the boat to Buenos Aires. It's very easy and can be done over and over, there is no limit.
One other good thing about Argentina, the dollar is holding steady with their peso. Unlike Brazil where it's dropped 25% in the last couple of years. If your goal is good living on as little as possible you can learn from the locals and really cut your expenses down. I did a little of both (living large for cheap) and cooking at home (for really cheap). My cost of living was 40% less then it was in Dallas, that's why I moved there.
If you are going for 6 months, make sure and get there for summer. If you want to be in the States for the Holidays then go down there in January. I like flying on New Years Eve as flights are always much cheaper then other days in that peak travel period. Jauary and February are great, the locals are all gone on vacation, the cities population is about 25% less then normal, it's nice and quite. The weather is nice and the outdoor cafes are everywhere and in full effect. You will meet plenty of expats (if you want to), they are everywhere.