I spent a few weeks in Paraguay with some of my wife's relatives. Part of the time was in Asunsion and part out in the countryside of Arroyos y Esteros. Her uncle was our tour guide and rather possessive self-appointed bodyguard for most of our stay. At about 4 foot something with a 45 strapped on his belt, he was good to go for the job. He had so many stories of robberies and such that we were a little on edge in the capital. One such story that kind of surprised me was his niece having her long hair stolen by a guy with a knife on a collectivo. But in retrospect I think he was maybe a bit overprotective, and probably the city is not so dangerous as he was painting it. However, to be sure, if you are somewhat obviously extranjero in BA, you will be doubly so in Asuncion. Some people are very poor there, so something that might not seem flashy to you might be very attractive to steal, and as usual you should be watchful.
It is not the same kind of tourist hotspot as BA, (but don't tell the locals that or you will be in trouble. If they ever ask you which you like better Asuncion or BA, tell them Asuncion is the most amazing city you've ever seen. Don't say I didn't warn you). Knowing Guarani would be nice to gain the trust of the locals, but I only met a few people there who did not speak Spanish- mostly they were older. The public schools teach Spanish and Guarani and it seems there are a lot of cognates between the two languages. By far the time I enjoyed the most there was out in the countryside of Arroyos y Esteros. It was so beautiful and relaxing, and the people there living a calm simple life. My wife had relatives there as well who took us in, so that meant all the difference as well. People were very friendly though, and strangers in the area pretty much welcomed us like family as well. I think you couldn't go wrong getting away from Asuncion somewhere to enjoy the countryside.
Oh, and one last word of advice - watch out if they ask you to play volleyball. At least where I was, they played it soccer style - no hands!! Thankfully I was only watching the game, in amazement.