How do I get to Cosmo Hotel Queen's road East , Wan Chai from Hong Kong Airport?

Well, there is no direct shuttle bus that can take you from HK Station to the hotel.
Thus upon arrival, you can take shuttle bus no.11 from the airport to Admiralty Station, Queensway. Then transfer to the Tram (Shau Kei Wan - Western Market) from Queensway (Admiralty MTR Station) to Hennessy Road (Tonnochy Road). After arriving, walk south around 300 yards to find the destination. The duration is 70 minutes. And the ticket fare is about 42 HKD per person.