Because Banff is not a particularly big town, it can't sustain multiple restaurants of the same style (with the exception of Japanese restaurants). While a big city, like Calgary, has a huge variety of Vietnamese, Italian, Spanish, Mexican, etc. restaurants, Banff has just a few of many. The "Mediterranean" options in Banff vary from truly authentic Mediterranean to nothing-particularly-Mediterranean-about-it. But, there are options from Greek to Italian to Spanish.
There are three places to go for tapas and authentic Spanish cuisine in Banff. These are all downtown. The Cafe Soleil is a tapas restaurant on Caribou Street, but it's not the only one. You can also get Spanish food on Caribou at the Magpie & Stump Restaurant & Cantina. Cafe Soleil is the more authentic Spanish place, though. On Banff Avenue, a good place for Spanish is Caramba!
For Greek lovers, Balkan: The Greek Restaurant is the leader in Banff. The other options, such as Athena Pizza and Spaghetti and Barpa Bill's Souvlaki, do offer Greek, but Athena focuses mostly as a pizzeria and Barpa's is not really a sit-down-and-be-served restaurant. These are all on Banff Avenue, though. In fact, Balkan and Athena are basically right beside each other.
Several Italian restaurants in Banff are quite good. Castello Ristorante in the Banff Springs Hotel is the on the high end of the Italian scene in Banff. You definitely pay for the atmosphere and service. On Banff Avenue, Giorgio's Trattoria is the most authentic Italian restaurant. But, for an Italian-alps experience also on Banff Avenue, Ticino brings in a hearty Swiss element to its food.
208 Caribou St.
337 Banff Avenue
Banff Ptarmigan Inn
405 Spray Avenue
The Fairmount Banff Springs
Alpine Setting and Italian Cuisine... read more
110 Banff Ave
Hearty pizza and pasta in the center of Banff...
219 Banff Ave
415 Banff Avenue
European Elegance with the inspiration of Ticino...
215 Banff Ave
304A Caribou Street