Woo Taipei in Zhongxiao Dunhua. Nom Nom near Shida.
The po boys at NOLA.
Toasteria; the new Dongmen one is very nice but make sure to get reservations. You could also try the cheesesteak sandwich down the street at Focus Kitchen. Nearby, Panos is OK, but not great.
These types of places are hitting on rough times, though. Mactugal, Cozi Burger, and Eating Time all closed not too long ago.
Speaking of Viet food, I've yet to find really good Viet sandwiches (or food) in Taipei. There are some OK ones about, like at Gongguan night market, and near Houshanpi MRT station. Coming from Texas though, the Viet food here is pretty mediocre.