It's not every day I get to talk about my speciality - cities - so I'm happy to jump at the chance. Unfortunately, I've never encountered any 'serious' proposals for cities in the sea.
I see some problems right away, though. Maybe these are addressed, but I'd like to bring them up anyway. Because cities are more than just a collection of houses, and they have a more or less distinct set of requirements and problems, both of which would be difficult to meet at sea. Not impossible, mind you, but difficult.
Of the problems I can see, most or all are problems of scale. On a small scale, this approach could be quite sustainable. On a large scale, however, it would require some radical innovations. Getting supplies to the city ( cities - at least the overwhelming majority of them - are net consumers, and require surplus production elsewhere ). You might be able to get over this problem with farming, or production of edible algae, and obviously fishing. However, this would be quite intensive on space, and would require even more potable water than what you'd need for people to survive. This is mentioned on a seasteading site I found, but it gives no exact figures for how much space would be needed. It does mention that soil would have to be imported, however. I don't know enough about farming to tell you whether or not you could then survive on the imported soil alone ( through fertilization and so on ), or if you might be able to create your own. More on this later.
Water, I think, would be the biggest issue. Unless you could set up large-scale desalination, or collect enough rain water, you'd by definition not be self-sustained. Desalination of seawater is extremely energy-intensive, so now you've replaced your dependence on transporting water with transporting energy. I'm not sure about rain water, but at the very least this would limit the geographical areas you could live in to those with sufficient rain. I don't know exactly what scale the city would have to be to cover all these needs, but it would be large. If you intend to do anything but
cover basic needs ( i.e. have businesses and homes and what have you ), you're looking at even larger requirements.
Energy is the next big issue. The site I found mentions wind, solar PV, and wave energy. I can see why. Solar PV has some very obvious limitations, in that they can only function when there's sufficient sunlight ( really, all the sources mentioned have some form of limitation based on weather conditions ). You also need space for it, which is a considerable limitation at sea - and you already need it for farming. You'd need quite a lot of it, too, if you're going to desalinate your own drinking water. Again, I really don't have the knowledge necessary to make the calculations, and I could be overestimating the energy needs versus potential energy production.
One thing I don't see mentioned on the site, which is going to be a huge deal in any community of sufficient size, is waste management. Using human waste as fertilizer is, from what I can gather, risky. Composting apparently helps, but it still should not be used to fertilize vegetable gardens - which is obviously what you want.
Then there's all kinds of scrap, excess salt water, and all other kinds of waste you need to get rid of. Short of just chucking it in the sea ( which would be a bad idea for reasons I think should be quite obvious ), you'd either need large-scale storage, or regular pickups. Which again goes against the idea of being self-sufficient.
Now, if you're not looking at being self-sufficient ... I suppose it could be possible. I think it'd be more practical as an extension of extant cities, than building new cities at sea. The technical challenges would be far greater than with a city on land, though, so it would be something to consider only in places with appropriate conditions and a real need for more space.
So, in summary: If you want to be even remotely self-sufficient, you need space, and people. If you want space and people, you have to scale up. Scaling up means the requirements grow. A properly self-sufficient city at sea would have to be of considerable size - and would be both technically and economically difficult to set up.
The free city of Christiania, in an abandoned quarter of army barracks near downtown Copenhagen, was much moreof a success story, sort of - and a haven of controversy (not least about the street called, tellingly, "Pusher Street" where you could, for many years, openly buy any dope you wanted). That one still exists today, more than forty years after the initial squatting, despite many pledges by Danish politicians to oust the folks living there.
You can still buy drugs very openly there. It's also a generally lovely and friendly place! If Danish authorities did evict people ( which no doubt they do, since the area is prime real estate ), I imagine the damage to Copenhagen's economy ( and reputation ) would be greater than the benefits. As someone with an interest in urban geography, and a frequent traveler to Denmark, I'd be really interested in seeing some analysis of the economic gains ( from tourism, and to local businesses ) generated by Christiania. I imagine it would be quite considerable.