I'm glad our comments have helped you feel more confident about your plans.
But, for the record, the ONLY reason I suggested not to climb the Tokyo Metropolitan Government Building in Shinjuku is because you are staying at the Park Hyatt, one of the nearby high rise buildings you can peek out on from there. There really is no need for you to go.
I am not usually installed in such a lofty perch and the viewing platforms at the TMGB are a looked forward to highlight during my own visits. As I said, seeing day turn to dusk turn to night from here is usually a magical experience. I don't consider the big atria to be "dumps", they are what they are, large public spaces, not the reception lobbies of a 5 star hotel. Particularly when musicians are playing, they can be a very pleasant place to kick back with a reasonably priced hot drink.