These suggestions are based on modifying the Civ 3 air system, so they may be way off:
1) Re-base should be a free move and not take an entire turn. This would tremendously increase the usefulness of air units.
2) After a certain tech(Radio?) you can assign fighters/bombers to 'close air support' for a particular unit. AS long as that unit is fortified/attacks within range, the aircraft will provide more powerful bombardment(more accurate targetting data, spotters). If they attack, they your units help in the attack. If they are attacked, same still goes.
3) You can assign fighters to escourt bombers on their sorties.
4) Nuclear bombers should be units that can only be used once for 'dropping the bomb'. They would cost less than equivalent missle systems. They are also avaliable earlier.
5) Transport Helicopters should be able to extricate troops as well as deliver them to the field. They can also transport Artillery(okay, it was light guns in Korea, but it was still arty).
6) Attack Helicopters should be able to have the same 'close support' abilities as Fighter/Bombers. They should also have mundo bonuses vs. armor. They should also be able to base more places.