Cities are generally not targets for high yield weapons. Multiple low(er) yield weapons do more damage to soft targets, like cities, than fewer high yield weapons. Additionally, they don't need to be as accurate for these roles. This is traditionally the realm of submarine-launched ballistic missiles: a countervalue guarantee against a first strike. The Trident D5's incredible accuracy and high yield changed that calculus a bit but that is a different post.
High yield weapons are used against hardened targets such as ICBM silos, underground command posts and launch control centers, communications hubs, leadership shelters, etc. The relationship between yield and accuracy is of course related, but at the end of the day counterforce weapons tend to be on the higher end of the scale. Earth penetration capabilities also influence yield choices, e.g. the B61-11 bomb @ 400 kilotons replaced the massive B53 @ 9 megatons. Both are bunker-busters, but the former bomb can penetrate rock and earth before detonating while the latter sits on the surface at detonation.
Counterforce vs. countervalue targeting touches upon some of your points. It's a long discussion but in essence the former approach is designed to reduce the ability for the enemy to effectively wage war, especially nuclear war. This means targeting command posts, communications hubs, air bases, missile silos, nuclear weapon storage facilities, etc. Countervalue targeting is meant to inflict unacceptable damage to the enemy by targeting power plants and other infrastructure, transportation hubs, and cities & their civilian population. Countervalue targeting requires far fewer weapons and lower accuracy, but it means direct mass murder of civilians a la the firebombing of WWII, rather than the indirect mass murder of civilians as a byproduct of targeting militarily-useful assets. A large scale "pure" counterforce attack would inevitably result in many civilian casualties though they were not the targets.
Oh boy, it's a huge subject. I'd actually start with the wiki entries on nuclear warfare & countervalue vs. counterforce targeting. The National Security Archive has some very good briefing books on the evolution of the SIOP which deal with the flexibility policymakers started to want over time as well as debates about launch on warning (where you fire once you believe you're under attack) vs. launch under attack (where you ride out at least some of the first wave).
Alex Wellerstein's blog is a good one and he links to other quality sources as well (though note some are decidedly abolitionist when it comes to nuclear weapons).
High yield weapons are used against hardened targets such as ICBM silos, underground command posts and launch control centers, communications hubs, leadership shelters, etc. The relationship between yield and accuracy is of course related, but at the end of the day counterforce weapons tend to be on the higher end of the scale. Earth penetration capabilities also influence yield choices, e.g. the B61-11 bomb @ 400 kilotons replaced the massive B53 @ 9 megatons. Both are bunker-busters, but the former bomb can penetrate rock and earth before detonating while the latter sits on the surface at detonation.
Counterforce vs. countervalue targeting touches upon some of your points. It's a long discussion but in essence the former approach is designed to reduce the ability for the enemy to effectively wage war, especially nuclear war. This means targeting command posts, communications hubs, air bases, missile silos, nuclear weapon storage facilities, etc. Countervalue targeting is meant to inflict unacceptable damage to the enemy by targeting power plants and other infrastructure, transportation hubs, and cities & their civilian population. Countervalue targeting requires far fewer weapons and lower accuracy, but it means direct mass murder of civilians a la the firebombing of WWII, rather than the indirect mass murder of civilians as a byproduct of targeting militarily-useful assets. A large scale "pure" counterforce attack would inevitably result in many civilian casualties though they were not the targets.