We took a pretty standard approach to seeing the sites in the short time we had there. Of course you can spend about a week in Harbin enjoying the many sites but you can also stuff it all in to 2 days.
For just 2 days the Ibis Hotel is convenient and cheap. You can organize your taxi from the airport through the hotel for 150CYN and they have the below-mentioned tour to the Snow and Ice World. It is walking distance to the pedestrian street and the Zhaolin Park.
Take a taxi driver for about 250CYN-300CYN who will stay with you for the morning. Get him to take you to the Sun Island Scenic Area where the Ice Sculpture Expo is. He should wait while you spend 2-3 hours there.
Then get him to take you to the Siberian Tiger Park. Here you can take the bus through the park, spend some time in the walking area and look around their tourist info/store. Pay the extra 30CYN to have an English speaking guide accompany you and get you good seats on the bus.
From here return to the hotel and rest up until the evening.
From your hotel you may find that there is a bus tour from the hotel to the Snow and Ice World at 4pm. The bus costs 30CYN each way and you get your entry ticket to the Snow and Ice World from the tour lady so you don’t have to stand in line to buy it once you arrive. Alternatively take a taxi to the Snow and Ice World in the evening. The site closes at 9pm and you will want at least 2 hours there.
Day 2 is for the Zhaolin Park festival site; exploring the pedestrian street; taking a walk along the river side and seeing the activities there; visiting St. Sophia Church and generally enjoying the city. You could also visit Polarland if you choose or the museums.