The Suzhou Sheraton has a hotel car that guests can engage and its cost is at least twice that of a taxi. We wanted a car for a day trip from Suzhou and instead of using the hotel car, we asked the concierge to arrange a taxi. I don't remember the cost but it was at least half or even less the cost of the hotel car and it was the nicest taxi we rode in during our entire time in China. However, the taxi driver did not seem to know his way around too well and some time was spent in backtracking and trying various routes. It may have been that he was trying to avoid tolls.
To arrange your own taxi, have the hotel write down the characters for the airport and your terminal, then show them to a few taxis that look reputable and see what they say. Have your calculator handy so they can show you the price. Also consider that some taxis have limited luggage space and you may be quite crowded for a two hour trip.
Happy trails!