And make an extreme health bonus for having a garrison in the city
Not a bad idea, but I don't know how to do that. It's probably possible with LUA, as just about anything seems to be. I'm pretty sure I can adjust city strength bonus when garrisoned and also base city strength, so I'll see about doing it that way. I don't plan on making it an extreme difference, but I will definitely test out adjusting it to a degree in favor of needing a garrison.
I'm a little confused on whether you're referring to the AI taking too long to capture cities, or if you find it too time consuming yourself. I would agree that the AI has problems for sure. Not much can be done about that unfortunately.
As Germany I've found things like mainland France and Norway completely conquered by about turn 5-7, and then Athens around turn 12 or so. Basically my experience is that by using air sweeps to clear interceptors I can come at a city with a few bombers and maybe an artillery or two. After that the city should go down on that same turn after a few infantry waves. Since you can stack them 2 per tile I can't imagine it being too difficult to capture cities. Especially if you keep in mind that I have already taken measures to make city assault bonuses higher in the next version.
So far I have made the following changes:
PROMOTION_CITY_SIEGE increased from 20 -> 33 (artillery units)
PROMOTION_CITY_ASSAULT increased from 50 -> 60 (infantry)
PROMOTION_BOMBER_SIEGE_1 increased from 20 ->25
PROMOTION_BOMBER_SIEGE_2 increased from 40 -> 50
PROMOTION_BOMBER_SIEGE_3 increased from 60 -> 75
PROMOTION_BOMBER_SIEGE_4 increased from 80 -> 100
PROMOTION_BOMBER_SIEGE_5 increased from 100 -> 125
I also reduced the effect of vanilla promotions like shock and targeting to a small extent to try and balance things a little. I think it will certainly be a easier to take cities though.
As for cities like London, Paris, Berlin, Moscow, or Athens then it should be a couple turns. IMO this is good, since those are capitals and they should heavily resist being captured. Losing a capital in this scenario, or any civ game for that matter, is kinda a back breaker. Regardless, I'll add in the city strength adjustments I mentioned at the top of the post and see how the new settings work out when I begin testing. I'm not sure when that will be though, as I want to complete the new map first. Hopefully setting buildings will go faster than I'm dreading.