Transportation from Harbin Airport to 80 South Fourth Street

If you refer to Nansidao Street in Daowai District, hope my reply help!
Take Shuttle Bus line 3 to Daowai Bus Station and then catch a taxi to your destination within 5 minutes.
The ice and snow world is about 8km west to the place you go first, and you can take another taxi to there. The fare is about 25RMB.

it is also possible to take a bus to the Ice world?

The bus is also okay. You need to walk north for 5 minutes to Daiwai Sandaojie and take bus 12/24/95 to Shirenda and then transfer to bus 29/47. Get off at Bingxue Dashijie (Ice and snow world).

Hi. I wonder if it is a good idea to stay at a hotel near West Railway or is it better downtown. Thanks

I think downtown is a better choice, and you can stay in Central Street.