"Gehen Sie die Treppe hinauf bis zur ersten Etage", to keep it as close to your text as possible, is correct German. Note that this is what you would say in a detailed decription that covers more than just getting to the second floor. An example would be "Gehen Sie den Gang entlang bis zur Treppe, dann gehen Sie die Treppe herauf bis zur ersten Etage, dann gehen Sie durch die blaue Tür..." "Gehen Sie die Treppe hinauf in den ersten Stock" is also correct. Note that here, the second floor is a destination. In the previous sentence, it was the location where you stop climbing the stairs. This is the distinction Cherry is pointing out. If you only want to tell someone that he should go to the second floor, you would just say "Gehen Sie in den zweiten Stock" as suggested above. (And you would not mention the stairs unless there are other equivalent means of reaching the second floor.) Please note that what Cherry wrote about dative and accusative in German is only true for prepositions that allow both, such as "in". In these cases, dative indicates a current location (where what the sentence describes is happening) and accusative indicates a destination (that is approached by something as described in the sentence). The preposition "zu" (and thus the contractions "zur" and "zum") require the dative. Unfortunately there is no simple rule that always works, but in many cases, when you use "zu", what you are actually saying is "go to the location of ..." or "go to a location near...", or as in your sentence, "go up the stairs until you reach...".