You should be able to find European names in at least some major department stores. I think in Canada one would be The Bay and in the US you might try Bloomingdales or similar. If you're in America I think they have US brick and mortar stores for the below retailers.
Zara and Mango are Spanish retailers. They have some nice pieces. Generally I find their fit a bit odd but I did pick up some neon pink pants a few months ago from Zara which I love. Pull & Bear is another Spanish brand. I think they are cheaper/lower quality; I don't shop there as I think it's for younger people.
Karen Millen is a British retailer which has nice clothes but more on the $$$ side. I ordered some shorts recently but it seems their quality wasn't great. It may be better for their dresses. I got a beautiful red trench coat a few years ago which was very good quality. Ted Baker has some nice pieces, good quality, but odd sizing. Reiss and Hobbs are also very good; I use them for work pieces and their quality is very good. French Connection, Topshop, Marks & Spencers, and Asos may also be worth checking out. River Island is popular but I consider them to be overpriced; they have many trendy pieces but they're expensive and you might be spending money on something that will go out of style quickly.
Cos is a Swedish brand. Their aesthetic is not really my aesthetic (more flowy than fitted pieces) but I think their quality is good.
Maje, Sezane, and ba&sh are all French brands, more on the $$$ side.
Sounds like you already know what you like; I found Pinterest helped me with specific pieces to look for in stores - I would pin things which looked good on me and look for common trends (like belted items).