I hesitate to say this is entirely wrong, it just doesn't seem right.  It sounds disjointed.

They could have left the tagline as "The best place for nails" even though it would be a duplicate of their business name.

Using "The best place in town" would still convey the right message and tie the exotic idea in with being local.  It would also add a second message of it being the ultimate business in the locality - perhaps not something they can prove on a supreme level but possibly on some level.

However the way that it currently is, breaks up "The best place in town" which we are used to hearing - it disturbs the 'rhythm' of the phrase. 

If they really wanted to keep all the words in the second line then how about "The best place in town for nails".

Instead as they have a strong business name that describes exactly what they do, two signage areas, and don't really need a tagline, they could use the sign real estate for something entirely different.

What about opening hours?  Contact details?  Something that further defines 'exotic'?  A website or Facebook page url, where they had examples of their handiwork?  An incredibly witty statement that makes you smile?