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I have 2 lists of words. One list has fruits names. Another list has cities names. I'm transforming it with word2vec and trying to classify resulting vectors. But it doesn't work.

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It is not necessary to use the neural network in such a simple problem. Use K-nearest neighbor (KNN) instead. That is, for a test sample, find the word from your training set that its vector is nearest to the vector of the test word, and assign the class of this nearest training sample to the test sample. If you want to use neural networks, which I do not suggest, you should have many training data to avoid a complex neural network from overfitting.

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