We had lunch in Montevideo on our last day at the Puerto Market. What a sight that was! So much barbequing meat! It's all grass-fed (since it's more economical for them, actually) and was so good.
It was a huge pile of grilled steak, chicken, pork, and sausages for $12, which more than fed two of us.
There are a ton of places in there to choose from, and they all have basically the same thing, so it's really up to you where you want to sit. We chose the one that has a balcony overlooking the square. Since they realize they are directly competing, they have like 'hawkers' or whatever you call those people that come up to you and say, "come into my restaurant." They may offer you free stuff to choose theirs.
Definitley go there when you are hungry!