There are numerous hotels and hostels located within walking distance to the Powerhouse Museum, that will cater to all budgets and requirements.
Some examples hotels are listed below, and a complete list can be found here [link]
Novotel Rockford Darling Harbour (4.5 stars)
17 Little Pier Street Sydney NSW 2000
Email: Sydney@rockfordhotels.com.au
Ph: 61 2 8217 4000
Oaks Goldsbrough Apartments Darling Harbour (4 stars)
243 Pyrmont Street, Pyrmont, Sydney 2009
www.oakshotelsresorts.com
Ph: 1300 667 078
Email: resgoldsbrough@theoaksgroup.com.au
Holiday Inn Darling Harbour (4-stars)
68 Harbour Street Darling Harbour, Sydney 2000
Email: info@holidayinndarlingharbour.com.au
Ph: 61 2 92910200
www.holidayinn.com
Vulcan Hotel (3.5 stars)
500 Wattle Street, Ultimo, Ultimo, 2007
Ph: (02) 9211 3283
www.vulcanhotel.com.au
Sydney Central YHA
Corner of Pitt St and Rawson Place (opposite Central Station) Sydney 2000
Phone: 61 2 9218 9000
Email: sydcentral@yhansw.org.au
Transport from Airport to Hotel
There are several options to get to and from your hotel. A uber or cab will cost roughly 50-$70 depending on the time of day and traffic. You can use the below tool to estimate your Uber ride
http://uberestimate.com
You can also get an Airbus Airport Shuttle bus for door-to-door service, prices start around $16/person
https://www.airbussydney.com.au
Or you can take the Airport Train, with an adult tick costing $17.90
http://www.airportlink.com.au/