"circle to the north side of the city, break down the gates, then heat for the barracks and burn them"
This leaves an interesting question of if we can actually "burn down" or separately destroy individual buildings during the actual battle and if this could have a negative effect on the Defensive player's bonuses (city bonuses).
For instance, set any one military building on fire, defenders lose 10% max bonus
set all military buildings on fire, defenders lose 50% max bonus
set city square on fire, defenders lose 25% max bonus
set over half the houses on fire, defenders lose 25% max bonus
also, sharing a tile with a burning building might cause you to take some damage. After a certain amount of turns a flaming building would turn to rubble (hot charcoal rubble), and after the battle would turn into harmless yet useless rubble tiles that have to be rebuilt upon.
Perhaps flaming arrows, flaming catapults ... and also perhaps infiltration units that are equipped with firebombs ... probably a near suicide mission, but with a chance to escape to the outside. Some "more expensive" buildings could be made fire resistant ... for instance if they were made with almost no wood, or rather made of Stone or Granite (I heard marble burns? is this true?) maybe buildings made of wet clay could also be resistant to burning ... but they would be more likely to be simply squashed flat.
Again, normal catapults (or flaming ones) might, if landing on a building, squash it flat. This would hurt the defender's bonus just as much as setting it on fire (however fire tends to also harm defenders' Morale). Only buildings could be resistant to being crushed, and easily flammable, or immune to flames but easily crushed.
In any case, actually interacting with the city (and potentially destroying individual buildings) would be cool, and if fires have a chance to spread it would be even cooler (in the city-> morale and HP penalties to the defenders)