Look in the Red spawnpoint of Dustbowl 1. As you walk in. there is a half-rolled-up world map on the wall. If you look closely (a sniper scope helps), you will notice that it it is an ordinary map except for the US, which is divided into many different pieces of varying colors. (Blue and red are the most common, of course.) In Granary, there are a few speed limit signs. They are written miles per hour and designed like they are here in the States. (Although this design may be used elsewhere, standard measurements aren't.) Of the 9 classes, at least 3 are obviously American stereotypes. (The Scout, Engineer, and Soldier are obvious, the Pyro is an unknown.) Finally, the architecture and landscape are similar to those of the Mideast and Southwest (of the US), respectively.
Because of all of this, I think it is safe to conclude that TF2 is set in the United States. Based on the huge computers and racks of magnetic tapes that are all over the place, and the other technology of the setting (the Engineer's buildings are an anomaly in terms of technology) it also seems to be set between 60 and 40 years ago, in a dystopia where ideological differences between the agricultural (RED) and industrial (BLU) halves of America split and broke out in a kind of civil war. Note that BLU is always attacking, and that industry overtook agriculture in the US during this period.(Sorry for my heavy use of parentheses.)