The second phrase, "take a vacation to abroad" wouldn't be used as whilst you're going abroad you're not going *to* abroad, you're going *somewhere*, so we'd tend to put the place name. The first and third phrases are fine, but tend to be used in different circumstances. "Take a vacation abroad" is the more regular usage as it simply refers to the fact that you are holidaying overseas. The third phrase "take a vacation to go abroad", tends to imply that the purpose of taking a vacation is to go overseas. The difference is quite slight and would probably be missed in most contexts, therefore, personally, I would tend to go with the first phrase "take a vacation abroad", e.g., "I have the next two weeks of work so I'm going to take a vacation abroad".