Dragons in early conquered territory.

Stay away from dragons. They're top of the food chain for a reason.

Alas, the AI loves to place outposts/cities in complete disregard to surrounding monsters. It's wise to scout out the territory before you make a quick conquest - some AI cities are more trouble conquered than left alone.

I've conquered AI cities only to have monsters released by the computer come and attack those cities - I end up investing in cities that are razed 2 turns later.  

I have witnessed in my current game roaming bands of monsters in a Wildlands area take out an AI army who came wandering in, at least this is on 'challenging' with 'challenging AI'  I cannot speak for higher levels of difficulty.  It maybe that the monsters ignore the AI on higher difficulty settings (part of their added bonus in production, etc).

it's always nice to have a sov (or champions) with earth 2 and water 2 - this allows you to use tremor and freeze to root some powerful armies. if you have enough mana, you can cast them with overlapping durations so you can root them in place infinitely (at least one army - you're in real trouble if there are more than 1 you can't handle yet).

when you eventually try to kill the dragon, life 3 can be pretty good if your caster manages to shrink it; death 2 can be somewhat useful for blind (though blind was nerfed to 25%). a high level defender hero with stun can be fairly useful too (or better yet- 2 of them, so they can stun-lock the dragon unless it resists). 

fire resistance spells/items can also be very useful vs. dragons (the earth spell that gives 20% +10% per earth shard can be really good if you have a few earth shards under control - it costs only 7 mana i think so you can buff your whole army before the fight and you can remove the buff afterwards if you want to save the mana maintenance cost)) to make their fire breath less deadly. on challenging difficulty, you can usually kill dragons with low-medium tier equipment  (leather armor, horse and boar spear is usually a pretty good combination) if your champions are somewhat powerful already (level 10+ with some decent items and abilities). on hard (expert?9 difficulty it's probably a bit harder, so i don't really know how strong you have to be to beat a dragon.

If it's an ashwake dragon, mage units with frost staves will quickly kill it, if you can keep the mages alive long enough. 

If you have a unit with maul, particularly juggernauts, they can really put the hurt on a dragon. 

Dragons are tough. wildlands armies ate through 6 of AI armies with Sovereigns each one of them.

I came in and cleaned up.

Dragons - maul damage, tanker, growth on him, and shrink on dragon.

and pray.

What difficulty was this on? The last Challenging game I played, there were dragons roaming around settled AI areas completely ignoring the AI player. I've even seen AI players and wandering monsters sitting on the same tile together with the number 2 above them sometimes.

Despite Frogboy's denial, the AI often DOES ignore AI cities and yet instantly attack human ones. I've had at least 5 different times where a powerful monster sat outside an AI city for the whole game. The instant I flipped it to my own, the monsters attacked.  Clearly the particular monster stack saw the AI city as nonexistent, just like it often sees AI armies on the same square.

AI cities get attackeed and razed. I've seen it happen. Also, I have seen dragons and obsidian golems dance around my cities, never attacking, just like they do with AI cities. It does seem that they attack AI cities less often, but statistical observation can be non-intuitive. Why would frogboy lie?

Agreed they do get razed by monsters. However, it happens less often. Like I said, I've had too many times where monsters attacked me only on a just-captured city. The instant they recognized I now owned it, they attacked.

Perhaps there's something in the monster AI that reacts differently when their lair is interrupted by a city/outpost founding versus a change in territory ownership?

What happens when you take over an AI outpost that happens to have a monster in it's radius?