I’m currently playing Civ V, and I like it a lot. I’m nearing a crossroads, and I thought I’d put it to a vote on what I should do. Bear in mind I have destroyers and helicopter gunships, they have knights and I think musketmen.
I’ll check back in to see if you are a merciful people or not.
How’s your empire looking on happiness? If you have some to spare I suggest grinding the bones of your enemies under the treads of your tanks.
What kind of city-state is it? With my play style at least, the bonus from allying with maritime city-states is ridiculously good, while (late-game) cultured city-states really pale in comparison.
I usually let City-States alone unless they are allied to my enemies and attack first. Buying their alliance with gold is usually the better solution. Knocking that smug Alexander guy down a peg, however, is always a good move. 
I don’t know Civ V, but I presume it has some corruption-like “your empire is too big” mechanic? It’s more economical to leave other civilizations alive but channeling their entire economy into your coffers. Sell them some resources you don’t need, or maybe an occasional obsolete-for-you tech.
Unless, of course, they declare war on you. Then, lamentations of their women, etc.
I think it is a maritime one. And Alexander really IS a jerk in this one-he’s insulted me at every turn. Most of the other city-states are my allies, so war would become a WWI scenario pretty fast. Perhaps I’ll just take one of his cities-I’m partial to islands. Happily the Chinese ruler seem sto like me a lot.
Civ 2 player here.
Let me get this straight.
- Your civ is late industrial. You can send chopper gunships all over the place. You probably have mechanized infantry and armor units, whatever the Civ 5 unit types are.
- The target civs are both pre-gunpowder.
This is a severe mismatch. I recommend the Dalek strategy towards both civs, subject to your happiness, corruption, production, and other internal limits.
(Note: The Dalek strategy is “EX-TER-MI-NATE!”)
I second the vote for leave them alone until they attack. Then nuke them from orbit, etc.
Greece is a no-brainer. It must be wiped out. The city-state, on the other hand, did give me a brief pause. But with a recent diplomatic defeat still ringing in my ears, I figure you might as well eliminate anyone who could wind up voting against you.
Here’s what I’d do: Cultivate an alliance with the city-state for the food boost. Invade Greece, and burn down any non-capital city of theirs that isn’t home to a wonder. Then found new, optimally-placed cities in the empty land that once was Greece. Your new cities should be up and running fairly quickly if you have lots of maritime allies and plenty of workers.
Aegina et illa urbana delendi sunt.
Beware of Greeks bearing gifts. In fact, it’s much safer to nuke them before they even get the idea of sending you gifts at all. Then you can tell the other civs you killed Greece because they were misers who never sent you gifts.