The observation deck at Roppongi Hills is a very romantic place to be in the evening. The view of Tokyo urban light is stunning.
There is a bar at the same floor (must be the highest in the city) with transparent walls and shelves, so you can go on enjoying the astounding view of Tokyo while drinking.
While you're there, look for the excellent views of the Tokyo Tower - the Japanese version of the Eiffel Tower. It's a classic Romantic view at night.

At the Roppongi hills complex (Roppongi station on the Tokyo subway).

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