Translation:She has a store in the center of the town.
In fact, there are differences. They may be rather of linguistic matter but actually "in the center of the town" is the best translation. Of course your examples don't really differ that much in meaning and I agree that they should all be accepted. But still, they all don't denote the same things, they are all slightly different:
"the town centre" is a fixed expression, an economic and social part of the city with certain properties. (Of course the place where a store would be expected most, but that would be reinterpretation and not what the term "centrum af byen" denotes here.)
"the center of the town" similar to the first one but not the same, as it denotes a loose description of the center of the town, without saying that it be "the town center" or just (rather) the geographical center.
"the center of town" wouldn't fit the Danish one because "city" is not definite here. It would denote an abstract and general "center of town" whereas here by determination a very certain one is meant.
Determination is used in utterances and texts to refer to a prior-mentioned noun. Thus, the city has been probably mentioned before. And then the indefinite noun "en butik" is newly introduced into the context and placed in the before-mentioned city's center. It is clearly a reference to something previously mentioned, without including the defenite article in the translation here the meaning wouldn't fit the Danish one.
"She lives in Copenhagen. She has a store in the town center." Of course, most people would interpret it correctly that she has the store in Copenhagen's town center. But that is not what the sentence says as it could also be understood that she has the store in another city's town center. It is not specifically referred to Copenhagen.
Sorry, I didn't want to come off as a smart ass. I am practically procrastinating and started a short answer and then it escalated. ^^ But as I said, I agree with you, that all answers should be accepted. The difference in meaning is not that big that they should be excluded.
Hi - Thanks for the long comment.
I guess I agree with most of that - just that when we say "the centre of town", we do usually mean a specific town (either the one we are in or the one we are talking about at the time) - "the centre of the town" wouldn't make it any more specific if we were in the country and didn't happen to be talking about a particular town.
There's also little difference between town centre and the centre of the town - if I said she had a shop/store in the latter, you'd be very surprised if it wasn't in the area described as the town centre. If you meant it was somewhere in the middle of the town but not in the town centre, you'd be unlikely to say something as misleading as the centre of the town - more likely you'd say "near the town centre".