Which of the sentences "go where you want to" and "go where you want to go" is correct? If both are not wrong, then what's the difference?

Assuming that the first sentence is meant to be "go where you want to" (and has just been typed incorrectly), while the second is "go where you want to go", both are acceptable in everyday use, as in the former the second "go" can be inferred from the structure (English has its share of contractions and abbreviations, of which this could be said to be one). Perhaps the second is technically correct (or at least is more formal). If formality matters, go with the second, otherwise use whatever is more comfortable. If, however, the first is indeed meant to be "go where you what to", this is indeed nonsense and only the second makes any sense.