You can target by country, even region within country so i believe, still about to get into adwords after a long break so dont have specific instructions unfortunately.
You can target by country, state, city or even zip code, but only on campaign level. You can select target location when creating a new campaign or edit targeting in the existing campaign - just go into campaign settings and find targeting section, then select areas you want to target. Hope this helps.
Can you really target zip codes with an adword campaign? How about post codes? Are IP addresses attached to zip-codes?
I just realized i was wrong about targeting by zip code - AdWords allows to search by zip code, but not target. For example if you search for 90210 the smallest area you can target is Beverly Hills, CA.