A and B are opposite statements. As you say, in standard English two negatives usually cancel each other out resulting in a positive. However in certain cases (often called double negatives, but that distinction is not always followed) the negatives are reinforcing or emphasizing. This is more common in colloquial English.
In the case here, A has a single negative, B has two negatives. They are opposite statements in my interpretation.
A is however not standard or acceptable English.
B is acceptable standard English English, also the following is acceptable English that has essentially the same meaning, with the negative moved.
There isn't anywhere I'd rather be than here with you.
An example of reinforcing double negatives include Pink Floyd's Another Brick In The Wall, that includes the line:
We don't need no education
.. but this is clearly colloquial rather than standard English.
Although in the linked question it's stated that double negatives usually cancel each other out, there are some exceptions. This case is not an exception -- isn't nowhere is nonsense and shouldn't be used. However, an even more attractive manner of expressing this is There isn't anywhere I'd rather be ... – barbara beeton – 2013-02-07T23:17:51.030
1@barbara, your comment tell me, at least as I understand it, that this question should not be closed as a duplicate. However I have opened a discussion on meta just to clarify what should it be the policy in case like this. – None – 2013-02-07T23:23:12.363
Related Meta discussion – Deco – 2013-02-07T23:38:21.027
1@barbarabeeton Not nonsense, I think. A is a denial of B. Carlo, for instance, may wish to qualify his statement that "There is nowhere I'd rather be than here with you" by saying "Well, actually, there isn't nowhere I'd rather be than here with you; there's somewhere: I'd rather be on the Champs-Élysées with you." – StoneyB on hiatus – 2013-02-08T01:42:45.660
@StoneyB -- with the addition of the two sentences you cite for context, i agree. but with no conteext, i still think it's nonsense. (sorry for delay. a blizzard intervened.) – barbara beeton – 2013-02-10T20:13:41.797
@barbarabeeton Yah, we heard about that. – StoneyB on hiatus – 2013-02-10T21:02:35.873