Hi, Mrs.Pitt, you could take the airport express and transfer to subway line 2 at Dongzhimen station, then shift to subway line 5 at Yonghegong station, get off at Dengshikou station and walk out from Exit A. Here, you could take bus No. 111 and get off at West Shatan Street(沙滩路口西), OR take a taxi to the hotel directly (costs around CNY10.00).
Otherwise, you may take a taxi from the airport directly; the taxi fee is around CNY150.00.

Hi staying in that vicinity myself in June and advice I got was van taxi works out best for 4 people,get the hotel to email you the address and phone mumber in Chinese to show to driver and take taxi from rank only, do not go with anyone who approaches you inside the airport, these people are not licensed