No trip to the West Side Market is complete without a trip to the Mediterranean Imports store. This place rocks.
They have one of the best cheese counters in the whole market, which is saying a lot, since the WSM is almost the only place to get amazing cheese in Cleveland. They may not have as many artisan micro-creamery cheeses, but the selection is still staggering, and definitely the best value. One cheese that I haven't seen anywhere else at this level of quality is called "Delice de Bourgogne." It's the best triple cream cheese I've ever had. Pick up a loaf of their multi-grain bread to go with it, and you have an appetizer or desert that will not be forgotten.
The other imported fare such as chocolates, oils, dried fruit, have all been excellent and reasonably priced. The staff is helpful and patient with the sometimes large crowds.
If you haven't been there, go!