This was made in a hurry, so it might not be correct at all as far as anything goes. But hey, there's a lot of numbers that no one else wants to calculate so I claim to be right anyway.
If we use the MIR submersible vehicle as a reference as far as for materials, we can break it down to this:
1 kg of titanium would cost about 26$.
A 12" x 12" piece of plexiglass with a thickness of .250" costs roughly 20$. We need 18 cm, or 7 inches. That raises the cost to about 560$ per 12" x 12" x 7".
I don't know how tall the buildings are in Rapture, but let's use the WTC as reference first:
The towers weighted about 144 million kg's per tower, and since they were pretty tall we can probably split the weight in half so that we come to a more normal-sized building. That's 48 million kilos worth of steel, and 24 million kilos worth of concrete. Steel weights more than titanium, so our building would probably use about 25 million kg's of titanium.
25 million kg * 26$ = $650 million
24 million kg of concrete = $1,56 billion
How much glass would a normal building need? If the building is covered by 50% glass, that makes about 7 193,25 m^3, which comes at a cost of $2,9 million.
Electronics, air-conditioning, and furnishing is hard to estimate, but let's guesstimate that the electronics and air-conditioning comes at a cost of $10 million. Furnishing is a harder topic, since the buildings seemed to be pretty snobbish in terms of interiors. Let's just come up with a number, let's say $25 million.
Other stuff like administrative costs for building it, etc? I don't want to know, but if 150 construction workers worked 12 hour shifts and made a building every 3 years, that would cost over 2 billion dollars.
We also need a sturdy foundation for the building, that's another couple of couple millions.
Estimated total cost of one over-water building the size of one half WTC tower: ~3 689 460 000 dollars.
Estimated total cost of one underwater city: probably a few trillion dollars, give or take. There's a lot of extra costs added when you go under water, add tunnels that connect buildings, etc.
Whoever built Rapture was filthy rich.