As a couple, Mori Art Museum & Roppongi Hills works.
A strong rotating programme of contemporary art near the top of a tower, with a combined ticket to the Tokyo City View deck — art plus a skyline in one stop, open late. The catch: it's exhibition-dependent (a show you don't care about makes it a pricey view), and Roppongi at night can feel like a touts-and-bars district.