PixelBoy: American Army used to be good, not sure how it's these days, as I haven't tried it for years.
But at least back in the day, it was a bit more realistic than most shooters, but yet had many good maps and lots of action going on. I guess the game is still around, so maybe worth checking out?
America's Army 3 is still around if i recall correctly, you can download it on Steam. But there's a new version coming out called America's Army Proving Grounds, which is in open beta at the moment(you can download it on Steam right now). I played it and i liked it. This new version is quite different to the previous games in the series. It's still more realistic than most shooters out there (it's certainly not COD), but it's more focused in close quarters combat than its predecessors. I mean, the maps on the previous America's Army games were HUGE (especially in the first one), in Proving Grounds the maps are smaller. But it's still a pretty good game.