depends heavily on faction. Heavy infantry catholic factions, I'll bypass field armies, and fight in the cities on both O and D, as heavy infantry tends to favor them. If I decided to invest more in cavalry this game, field engagements to outflank and route the enemy.

As eastern factions, 'weakened' HA armies intentionally lay siege to a city, forcing field armies back to engage and be annihilated by superior tactics, eliminating both the city and the enemy force. Generally speaking I'll almost always siege the city and either actually attempt a heavy infantry siege or else weaken my force enough to entice the computer to counter-attack.

For very heavily guarded citadels and fortresses, I'll simply bypass them and attempt to draw their garrisons out in the open, then either engage in the field or else force them to attack my besieging army. It's certainly a lot preferable to besieging a full stack in a 3-stage death trap. However, I see little value in open terrain most of time and beeline it for the cities. If the enemy has superior forces, I'll still tend to go around them, and meet them on grounds of my choosing when I want to.

If I can only attack one target, it'll always be the richest target I can take with the fewest casualties. A 3-unit defended fortress is preferable to a 10-defended city, but a 5-defended city preferable to a 5-defended fortress, assuming everything else is equal. I'll always take the nearest target of opportunity. The onyl thing that would give me pause is strategic map considerations that may leave other well-developed boarder settlements vulnerable, but the computer usually scrambles back to retake what it lost (especially provinces it considers key) that typically you don't have to worry much about counterattacks, so I don't mind sending my forces deep in in order to take key, high value, poorly defended rich coastal cities. The computer being what it is, I tend not to see how to hurt the computer the most, (As a faction) but rather what would benefit me as the player the most (rich city, castle for resupply, etc), but always it should be a defensive battle (ie AI is attacker) in their lands.