What place does Mrs. Gibb long to visit?

I believe you're referring to the character of Mrs. Gibbs from Thornton Wilder's play Our Town, as there are no characters of that name in "Town and Country Lovers."
Mrs. Gibbs, the doctor's wife, is unique in that she's the only character in the play who expresses a desire to leave the confines of Grover's Corners. Everyone else seems perfectly content with life in this small New England town, which inculcates a parochial mindset in its inhabitants. But Mrs. Gibbs is different. During one of her regular chats with Mrs. Webb, she reveals her long-held desire to visit Paris.
One can see why the denizen of such a small town would want to visit a large city, especially one as exciting as Paris. For Mrs. Gibbs, as for so many others, the City of Light is the epitome of glamor, culture, and sophistication, all the things her humdrum existence sorely lacks. Sadly, Mrs. Gibbs will never get to fulfill her life's ambition. By the time we reach act 3, twelve years after she reveals her desire to visit Paris, we discover that she's died of pneumonia.