I realise that turn lengths, in years, are kind of an abstraction (as Trip says), but those lengths are part of the 'immersive' nature of the game-making you feel like you are a real part of history (wheras a mere turn 1, turn 2 etc approach just wouldn't do it for me!) So, though I definitely feel that realism should give way to gameplay, there MUST be a way to make sieges work from both a realism and gameplay perspective!
I think the solution could be to make 'Siege Warfare' an extension of normal warfare, with the object of the 'attack' being the city rather than the troops inside it.
Essentially, if units fortify near an enemy city, in such a way as to create 'siege conditions', then when it comes to the combat step of the players turn, siege combat will be initiated.
Certain units gain a natural bonus (or penalty) to their attack strength for siege purposes, and other 'units' grant attack/defense bonuses to units for seige purposes (this goes for units in the besieged city as well). Certain city improvements will also give defense/attack bonuses to units inside the besieged city.
Basically, a city will have a 'Hit Point' value based largely on its size, population and location. Each combat 'pulse' the besiegers will get a 'siege attack' which will do either (a) nothing (a miss), (b) damage a unit, (c) cause a civilian death (d) destroy a city improvement/wonder or (e) reduce the 'Hit Points' of the city. The defenders will also be able to counterattack each pulse. Between each pulse, a morale check is made against the current 'hit points' of the city-varied by happiness, ethnic mix, distance from the capital, and government/religion factors-to determine if the city surrenders to the besiegers. Clearly, however, if all a city's defending units are killed then the besieging unit which scores the kill moves into the city and conquers it. Also, if all of a city's population die, then the siege continues until any defending units are killed or forced to retreat, which will allow the besieging army to take control of an empty city!
Hope that makes sense!
Yours,
Aussie_Lurker.