I assume by "330" you mean "330pm."

Right at the hotel there is little but underneath the nearby Hilton there is a shopping mall called "Hiltopia." Dunno what's there but there's bound to be something suitable.

I think the top of the Sumitomo building tends to have more pricey places.

The other alternative is to take the regular free hotel shuttle bus to/from Shinjuku station and you'll have a zillion options. I think the shuttle runs until about 9pm or so.

Pickles, I would have absolutely no idea how to find your kushiage place from that website. Maybe if I read kanji, but I don't, and I bet the OP doesn't either. However, I do know that shinjuku 3-chome is on the OTHER side of the station from the CH, and hence not so close, right?