Use your Giant Death Robots to take the cities if you're having problems with enemy air units, try using Mobile SAMs, Paratroopers, or fast units like Mechanized Infantry or Modern Armor instead. Any enemy units will be obliterated by your flock of bombers as you walk your melee troops into city after city.
Once you have a sufficient force of Stealth Bombers, the hardest part is marching your melee units fast enough to capture the enemy cities that your bombers are blowing to bits.
Before too long, your stealth bombers will have both Logistics and Air Repair, attacking twice a turn and healing 20 HP at the end of the turn in their cozy cities far from the front lines. They'll take some damage every time they attack, but you never need to worry about them being destroyed: they're sitting pretty at least 10 hexes away from the action, so when they're low on health, have them rest for a few turns. Better yet, each of their attacks is a melee attack, so they gain XP quickly. They have a range of 20, and a strength sufficient to damage any unit in the game. You'll get the ultimate end-game unit a few technologies earlier than the Giant Death Robots you're using now: Stealth Bombers.
