DinTaiFung

Cost actually depends on where you are, if you are North American or European visiting Taiwan, they will seem cheap to you, as everything seems cheap in Taiwan. Compared to other restaurants in the area though, DinTaiFung is a bit more high-end. DinTaiFung is now available in many other countries, but since it originated in Taiwan, I would mark the Taipei branch as more authentic.
Go for their small steamed dumplings, and that's it. That's their signature dish, and it's the best of the best. Of course taste varies by person, but most people consider the premium steamed dumplings to be thin crust, fresh meat and FULL OF JUICE. You certainly don't have to spend a lot of time looking at the menu!
Reservation would be recommended at this branch but you may still be required to take a number. Allow yourself time for the queue.