I use a backpack style carry-on luggage called the MEI Voyageur. This pack has served me very well over the last 3 years on multiple trips and very durable. It fits 3000 cubic inches with an internal frame and is so durable that you could probably do some light backpacking with it. It is made to the exact carry-on specifications.

The problem is that when waiting in long lines at the airport it absolutely sucks to have a backpack on and no one ever measures your carry-on with some exceptions like in Singapore or Australia. Also running around the airport with a pack on just gets tiring and old after a while.

The MEI pack is also too big to serve as a daypack and so you have to pack another pack within the MEI.

Another solution I have recently found is the Osprey Meridian which is constructed as to be a few inches larger then the maximum allowed. So it comes out to 3600 cubic inches which is 20% larger then my MEI pack. It also has a detachable daypack so you dont have to pack a seperate small pack. It has backpack straps, but the wheels can sometimes dig into your legs/back. Since you wont be using it for hiking, that wont matter. I just use the backpack option when exiting the plane and airport and getting over rough terrain. When I stand in a line, then I use the wheels.

http://www.backcountry.com/osprey-packs-meridian-22-wheeled-convertible-backpack-3600cu-in