Now, the biggest problem involved in building a city like Rapture wouldn't be material costs, but mainly the construction of the huge undersea dome it all resides in. Not to mention the fact that Andrew Ryan saw fit to build it all atop an active undersea volcano, which would have to be managed to avoid overpressure etc.
Now, say he constructed the outer hull on land. I'm going to make a liberal guess here and say that with respect to the size, the structural integrity needed and the absolute minute precision with which it would need to be created, i'd say he'd be set back at least a few billion dollars.
Sinking it would provide the second challenge, but like british naval forts, it's possible to just sink it from the surface and employ a few buffers to be crushed when it lands on the bottom of the ocean, and perhaps use a set of guide-cables attacked to the sea floor by submarine.
If you have a system of cables attaching this blob VERY strongly to the sea floor, a tight seal with the bottom would be redundant, negating the need to place the blob on level ground or rock. Just make sure you maintain those cables daily to adverse the threat of everyone dying instantly when they snap loose.
Then you'd have to pump out all the water, which could prove pretty easy if you had a team of divers in submarines with the equipment needed, carefully monitoring the stress on the cables to avoid the blob resurfacing.
Then, you could start building your city, complete with streets and all. Either you could build from a metal ring that lines the bottom of your blob, maybe even complete with a grid of iron bars to build a net of streets on that was attached prior to submersion, or you could build stuff on the sea floor, up into the blob.
The whole lighthouse elevator thing, i won't go in to.
All in all, i think it could be done for under a trillion, but the maintenance needed would be HUGE, as perfectly demonstrated by BioShock itself.
Superpowered mutants would make the whole construction and maintenance easier though.
