some clothing shops behind the SOGO complex in Causeway Bay shut close to midnight... if that's what you want (along Lockhart Road near SOGO department store)

otherwise, it's food drinks bar or the "things" between 2300 and 0900.

a few dim sum places open at 5am - Lin Heung Tea House and Luk Yu Tea House to boot.

I'd say Conrad, it wont take more than 30 minutes from Conrad to HK Station by cab. (ask the hotel when you leave. 30 minutes is terribly overestimated, it should take only 15. If they found traffic is terrible, take the MTR from the complex under Conrad to HK Station - assuming you will only have minimal luggage since you could tag thru your bags.)