This. If you find atomic bombs overpowered, wait until you see nuclear missiles. Rush-build 2-3 of them, and unleash the Apocalypse. Nuclear missiles can be sent nearly anywhere, EVEN IF YOU CAN'T SEE THE POINT YOU ARE NUKING!!! (sorry for the caps, won't happen again). If you have scouted their land thanks to a previous "open borders", you will know where their uranium resources are. Nuke them. That will even give you a fast view of what's there, so you know what you are destroying. Keep doing this until you have destroyed all their uranium resources. If they somehow still have a standing army (A-bombs take 5-6 hps from units, nukes simply destroy any unit whithin 2 hexes of the landing point), and you still want to take a random city from them (which will have half its population now, and momentarily half or less its hp), you can go now, it will be a walk in the park.
I usually try to play without them, but when the nuking rhythm reaches its climax, I simply have to, especially if the nuker lives in the same continent I do (if not, you can always "build" a wall of destroyers around you continent to see their atomic subs coming...).
2. If it's deep in their territory, good luck.
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Number four there is the only guarantee-- win the game before they get the chance to get nuke-happy with you.
For the resource spots issue, refer to the previous paragraph.
I usually play with diplo victory disabled (since there's simply no way an AI will beat me to that on the difficulty levels I play, but I rather not give them more science boni that they already have), so it's hard to win before modern era wars start raging everywhere, and I can tell you it ain't pretty. On the other hand, I've never seen the AI build a nuclear missile, only A-bombs...
If using nuclear weapons used up definitively the uranium resources (a random uranium spot loses 1-2 resources when using them), then nuclear weaponry would be balanced. Right now, with enough gold, 2 uranium resources means one nuclear missile every turn... As proposed, another way to balance them would be to radically increase their uranium consumption, and make them un-rushable.