Hello,
I'm a huge player of Civ1 and I must say the first tactic works but takes too much time.
And ALWAYS go for the capital!
Senario 1
You want a city that have a good defence and citywall and you are still in peace with that nation.
Build one diplomat and put it on a square where you ussually are no allowed to go.. before move the diplomat again, place a unit (whatever) and move the diplomat to another space. Do that until all squares are taken. Of course take squars that gives a lot of food and shields first. When the city is going down.. either take teh lat defending unit with heavey troops like Catapult, Canon etc.. or build those 4-5 diplomats it takes to destroy the citywall. Remember that a few unit doesn't care about citywall

artillery/robotics units.
Senario 2
You want a city that have a good defence and citywall and you are in war with that nation.
Build defence tropps and put them close to hte city you want to conquer, if there is mountains or hills nearby.. put them there in case the city you want have strong attack units those will die. Even a phalanx has a big chance to beat a tank if the phalanx is on a mountain and fortified (F)
Steal squares that gives food and shileds first.. and then do like Senario 1 and you have the city.
And like others has written, when the cpial has fallen.. the other cities it easy to buy. If you have no money.. sell buildings from taken cities and buy with that. Cities that are revolting is always MUCH cheaper.. go or wait for those
Another interesting thing with buy cities... if the city cost more then 65535 you GET money when you buy a city.. try to buy a LARGE city from a country with lost of money..
