Punta Arenas is a horrible city. Except one interesting main market place and a pretty cemetery there is nothing at all attractive about it. The main tourist attraction is a carriage museum. A nice spot, but apparently not worth the visit.
These days, the situation is even worse due to the upcoming local elections. The whole city is covered in signs and all kinds of propaganda, with happy faces of politicians screaming at you from every free square meter of the town. There is even this guy called Domingo, who collected more than thousand tires, lined them up along all major roads and attached his face to it.