Cooperative? Obviously you are some sort of a left-libertartarian, promoting such socialist nonsense.*
*Sarcasm
Business improvement districts, homeowners’ associations and the like could purchase a controlling interest in water and other infrastructure to prevent unwanted monopoly pricing.
How did he buy it?
If it is profitable, then some one will compete, and they will figure out how. Entrepenuers are very good at that. Maybe, in the absence of government regulation, above-ground pipes could be used again and would represent an enormous cost savings (enough to make it profitable). It is a hypothetical situation, and there is no way to know what solutions millions of people in NYC (or other city/locale) may or may not come up with. To know this would require omniscience- and not having that, in short, is the main problem with central economic planning.
All of the responses so far essentially say: The market would provide and would provide better than government. Of course it would, there is no doubt about that.
However, the real crux which I regrettably made halfway into the discussion, is larger than that, and perhaps should be a separate thread; and that is:
How can the currently state monopolized services, which the majority of city dwellers rely on, be provided during the transition from a state control to no state such that the people affected, which have no strong feelings toward either state or anti-state policies (which would likely be the majority), would be impacted most minimally in order to prevent a widescale rally and reorganization of a state like monopolizer?
Run on much? 
The solution to this has been presented several times in this thread. The people could form a cooperative that owns the lines, and they can select a private company to facilitate the service. This invites competition and lower prices. Further, if the private company is not providing the level of service the citizens require, they fire them and hire a new one. Other companies would be allowed to come in and build up their own above-ground lines, or perhaps there would be a leasing arrangement between the citizens (who own the lines) and several different companies (such as with deregulated electricity in places such as Texas). Not a perfect solution, but you cannot ignore that the infrastructure is already built. Might as well use it.
It seems like in order for those solutions to gain momentum they would have to be equal to or superior to the state production for the common man, in that, the effort put forth by the average Joe would have to be about the same (flip a switch, turn a faucet). Do you think that would be the case?
Remember please that I am generally talking about the average joe who doesnt know a utility function from a utility company. Maybe I dont have enough faith in the average person but I can see my current neighbors agreeing to organizing a coercive state over doing a little extra work themselves.
You need only look at the places in the US this has already happened. Water service has been privatized in towns, as has been discussed on this forum before. Average joe doesnt know or care a thing about it, but he notices when the water price goes down, and when the weird taste from the rusty lines goes away because the new private company fixes them w/o raising the rates. Just because you’re in a HOA by virtue of living in the neighborhood doesnt mean you have to be involved in its operation. The same could apply to this situation.
See Macfalls answer. There would be no monopoly without the state. All monopolies exist because of the state. People most certainly can dig more holes to divert water.