The answer to this question suggests that t-SNE should be used only for visualization and that we should not use it for clustering. Then what is the good use for t-SNE?
I don't agree with this conclusion. There is no reason to assume that t-SNE is any worse universally than any other clustering algorithm. Every clustering algorithm makes assumptions about the structure of the data, and they can be expected to perform differently depending on the underlying distribution and end use of the reduced dimensionality.
t-SNE like many unsupervised learning algorithms often provide a means to an end, e.g. obtaining early insight on whether or not the data is separable, testing that it has some identifiable structure, and inspecting the nature of this structure. One does not need visualization of the t-SNE output to start answering some of these questions. Other applications of lower dimensional embeddings include building features for classification or getting rid of multi-collinearity to improve the performance of prediction methods.