"We are going to the museum now."
Translation:Idziemy teraz do muzeum.
It's technically correct, of course, but it does not seem very natural to me, unless there's some specific context. "Idziemy teraz do muzeum" is neutral. "Idziemy do muzeum teraz" gives a strange emphasis on "NOW" and looks to me like a calque of the English word order.
Many things are 'correct' = 'not wrong', but not every one of them is worth accepting. Some things are just natural, some are not. We should try to keep to the first ones.
Is the "teraz" even needed given that we have been told over and over that "Idziemy" implies we are going right at that specific time? It would seem that putting teraz in the sentence at all is an emphasis on now. Am I correct?
It is a question of emphasis. the english sentence also ends with "now". So... "Idziemy do muzeum teraz." should be accepted!!! :-/
The rule of thumb is that "do" + Genitive is rather used with buildings that you can enter and "na" + Accusative is used with open spaces. But that's very far from being a strict rule. For example you also have "na pocztę" for "to the post office" although it's a building. Or "do lasu" and "do parku" for "to the forest" or "to the park". Hmm, the more I think about it the worse this 'rule' seems :D