The mall near the airport is International Plaza. It is an upscale mall, opened a week or so after 9-11 so has struggled a bit. The Lord and Taylor store closed, but I think that is a L&T issue. There is a shuttle to the mall, it is through the Renaissance Hotel. No need to be a guest there, just hop on and then walk up the steps to the mall.
I have eaten at the Cheesecake Factory 4 times and have not enjoyed myself. The food quality lacked. In defense of CF, I have eaten CF here is Scottsdale at Kierland and had a very good experience, perhaps management issues.
Bamboo Club is very good and would recommend, but as others mentioned go to Bern's for a non-chain non-mall experience. There is only one Bern's. The desert room is a wonderful, romantic experience. Be sure to ask for a tour of the kitchen and wine cellar, it is interesting and brief.