Being English and not American the only time I would refer to "stores" would be department stores "áruházak" otherwise I would always use shop/s üzletek/boltok.

With reference to the word "tall" department stores would spring to mind and not shops

I wrote - Az uzletek em magasak, apparently wrong word. I should have used boltok?

I wrote "nem magasak az üzletek". Why would that not be correct?

I guess "áruházak" should be accepted .

Yes, you are right!