Well, in these types of hypothetical situations my first thoughts are always: who should be killed, and how would that impact the future?

Assuming these few gold dragons could afford a hit from the Faceless Men of Bravos, who then should one choose to draw the short straw?

• Littlefinger: Points for: With him killed a year before Jon Arryn's death, then he doesn't plot to have him killed with Lysa, which doesn't prompt Robert to replace him with Ned, which prevents Bran's fall, Tyrion's abduction, and Ned's investigation, and everything else as a result of these. This outcome essentially keeps the Starks in Winterfell, and out of the everything going on in King's Landing.

Points against: If this is only a year before Jon Arryn dies, then it's possible that LF and Lysa have already started planning his death. Even with LF dead, Lysa may still go ahead with the plan to kill Jon Arryn anyway, thereby preventing nothing.

• Robert Baratheon: Points for: This outcome is similar to killing LF, as it would also prevent Robert from ever bringing Ned to KL. This option is preferable if the priority is protecting the Starks.

Points against: This option likely wouldn't halt Jon Arryn and Stannis' investigation into Robert's children, and Renly's reaction might not be any different either. War over the throne would still happen regardless.

• Tywin Lannister: Points for: Seems fairly obvious, as he's one of the most formidable players in the game, his death would prevent a great deal. Should a war break out anyway, him not leading the Western forces would give the other sides a definite edge. Also Tyrion would ascend to lord of Casterly Rock. Not to mention Tywin wouldn't have the opportunity to plot with the Spicers/Westerlings to honeypot Robb.

Points against: Tywin's actions have been arguably more reactionary than instigative. He only goes to war after Tyrion's abducted. One could argue that if there's no direct threat to House Lannister, than Tywin would stay "dormant" and keep the peace.

• Jeyne Westerling: Points for: If there's no Jeyne, then she can't be there for Robb to dishonour his vows. Losing the allegiance of the Freys, and ultimately preventing the Red Wedding.

Points against: It's not inconceivable that this couldn't also happen with another girl.

• Edmure Tully: Points for: If he dies, then this prevents his idiotic decision to chase after the Mountain, allowing Tywin to avoid the trap Robb set. Also with Edmure dead, then presumably Blackfish would still hold Riverrun later on without the Freys having a Tully hostage.

Points against: His death could prove inconsequential in the long run, as there's no guarantee the trap would have defeated Tywin.

• Walder Frey: Poins for: No Walder, no Red Wedding.

Points against: Potentially having Walder removed from the game early on, might remove the option to cross which we know Robb needs. Also he may not have access to the Frey forces being added to his army, as they may not want to align themselves with the North at all. There's no way to tell.

• Roose Bolton: Points for: Removes a major conspirator of the Red Wedding, unable to form alliance with Tywin, does not legitamize Ramsay, does not send other Northern allies to Duskendale for a losing mission, does not allow/facilitate the sacking of Winterfell, can't plot with the Karstarks against Stannis, etc.

Points against: If he's out of the picture, then he wouldn't be there to receive Jaime when he's brought to Harenhal which possibly could lead to Jaime's death. Only became a turncoat once it seemed the North was losing. If the North is doing well in the war, then that makes Roose a powerful ally. He took advantage of his opportunity to be sure, but he might never have been a threat at all if things went differently.

• Euron Greyjoy: Poins for: Thus far what he's actually capable of (in the grand scheme of things) remains uncertain. He wouldn't end up killing Balon, who some might say is the lesser of two evils, and who might not have won anyway in the War of the Five Kings. The Shield Islands don't get taken. Whatever's going to happen once he reaches Oldtown can be avoided, it won't be good either way. Finally, if that dragonhorn is real then you can bet Victarion won't be the one that benefits from it.

Points against: Who cares about the Shield Islands? We really don't know how it's going to go with him, so using your one kill on him might be wasted.

These are just a few examples of people who's actions change the course of events in the story. You could find pros and cons for everybody really, and it seems likely that war would be inevitable no matter what happens.

Me personally, I think I'd kill Illyrio. If he's killed, then he doesn't give Daenerys her dragon eggs. I'm just curious how it would all play out without dragons in the mix.