If you want to try traditional Bolivian food in a more gringo friendly environment we suggest Plaza Mayor which is located on Calle La Madrid halfway between the main plaza and the Cathedral.
El Marques is located on La Madrid on the main plaza. The good service, extensive menu, very elegant surroundings, and reasonable prices make this a great place to eat. A table by the window allows you to watch life go by on the plaza, or otherwise try the table upstairs which gives you the feeling of being elite and special.
For special occasions and truly elegant food you must go to La Taberna, a French styled restaurant on Ballivian between 15 de Abril and Virginio Lema. Although a little more expensive than the other restaurants you get a good selection of beautifully presented mains, outstanding deserts, and attentive service that makes this place value for money.