Soan's answer raises some really good questions that deserve answers. I was gonna make this a comment but it got way too long; so, full credit to him for what variables to consider.
The ideal place to build cities would be on the continental shelf within a few kilometers of the shore. While this would not put it in still water, there are many logistical reasons to do it this way. First is that these cities are built by land dwelling people; so, the closer they are to these now defunct infrastructures, the easier they are to build. Secondly, is that if you try to build past the shelf, you would be building on a cliff side of the continental slope which would be much more risky in the case of erosion, and the abyssal plane is way past the crush depth of modern submarines (that have large enough of interiors to support long term life). Apart from being at non-crushing depths, this also ties into the power grid issue because you could build hydro turbine power farms around your city to harness the tidal current of the continental shelf.
For building materials, you could replace steel with aluminum. Unlike iron alloys, when aluminum oxidizes, it becomes stronger; so, structures made out of it would be able to last for centuries under water. There is also the option of using portland cement to make concrete structures that cure underwater. While not as watertight as aluminum, this would solve your erosion issues. By planting your aluminum structures in heavy, porus, concrete foundations, your foundation would become overgrown and built up with coral faster than it erodes. As for structural shapes, while a dome (or sphere) is an ideal shape for underwater construction, you are likely picturing a giant glass dome but that creates a lot of seams and structural issues. The most logical configuration would be a series of hundreds of modular, interconnected, submarine like structures with plain metal or polymer exteriors, concrete bases, and minimal portholes and waterlocks.
While things would grow all over your exterior (bacteria, coral, barnacles, etc.) it would not make for any hernderance to survivability. Over-time, your city may be completely buried by sediment and coral, but things that are often used like water locks for your mining subs or outlets for bilge pumps would be be used often enough that they would stay clear with occasional maintenance
As for temperature, the average depth of the shelf is ~140 m (450ft), but only the top 100m of the ocean are particularly affected by surface whether. At 150m, the temperature does not vary nearly as much; so, where on the land might see an 80deg variance throughout the year, at this depth, your variance would be so much smaller that it may always be a bit warm, but you would not see fatal heat waves like on the surface. Also, photosynthesis is possible at depths of up to 200m, meaning you can farm with sunlight at this depth (though probably using specialized low-light crops or seaweed farming).
If you want to make "advanced" civilizations; you could have them build in the deeper waters in the Abysmal plane. Instead of hydro-turbine power, they could harness geothermal power and mine the exposed bedrock of the continental rise giving them access to vastly more power and resources. Their structures would be similar in shape and layout but be made from much more advanced materials like graphene laminates to be able to endure the greater pressures.
As far as plot hooks, it's pretty easy to see how superstitions and mistrust would build overtime between the high-born people who live in the light of the sun, and the low-born people who live in the total darkness of the abyss.
As for industrialization, unlike a space station, these colonies have the option of building "smoke stacks" that lead up to the atmosphere. This means that you could pipe in the Oxygen needed for your smelting equipment. While this air may be toxic and rather hot, it would still be suitable in a closed system for doing all the industrial things you can do with an abundant atmosphere on the surface.
This also means when mining or expanding structures, you can just pipe in more air to fill the new spaces after cooling, filtering, and compressing it.
With this in mind, I suspect mining would look one of three ways depending on the resource. One type would involve making a waterlock a little bit away from your city that just leads to a tunnel going down deep enough into the bedrock to make for a mostly airtight seal. Then you would use bilge pumps to clear any water that drips through and fill the tunnel with air conditioned surface air as you expand it. The second type of mining would be for the silicates and diatoms that make the actual sea bed which would probably just be shoveled up by specialed submarines. The third type would be for things that you have to return to the surface for. For this people may need to go back to land in what basically look like EVA suits to mine for things that may only accumulate under non-sea bed conditions or to recycle rare pre-fall materials that they can not manufacture with their limited surviving tech.