More model than computer, but from 1939 to 1972 there was a water driven model of the Mississippi River basin used to solve the flood models. It covered 200 acres (a little less than 1 square kilometer) and was useful until computers replaced it.
https://en.m.wikipedia.org/wiki/Mississippi_River_Basin_Mode...
It is unmaintained but is now a park and can be visited.
The University of Cambridge has a Phillips machine that works, if you're lucky it's even possible to get a demonstration. Here's a video of a demo given in 2010:
https://sms.cam.ac.uk/media/1094078
One interesting thing is that by attaching markers to the floats, and turning spools of paper on motors, it's possible for the machine to draw graphs as it operates.
you can see the moniac running if you happen to be in wellington on the first(?) friday of the month. there's a refurbished one in the foyer of the reserve bank (invented by a NZer - while employed in another country of course).
Only partially off topic: I like the picture "Etienne Dupérac's bird's-eye plan view of the gardens at Villa d'Este, Tivoli" in the article, and (other than the fact that it can be seen as a giant water computer) specifically those multiple maze gardens in there.
The fact that there are multiple maze gardens in there makes me think that maybe this was not as a cool attraction, but with the actual purpose of someone being able to walk all the way to the center of it, sit there with a book or so and have some actual peace and quiet time without too much disturbance of others?
That's quite different from todays always connected world :)
A more in depth version of this article that covers more examples: http://hplusmagazine.com/2013/05/10/gardens-as-crypto-water-...
In Sir Terry Pratchett's novel _Making Money_ there is a hydraulic analog computer used to model the economy of Ankh-Morpork[1]. Sounds very much as if Pratchett might have heard of this Russian one. However according to that article, the Glooper was in fact modeled after another hydraulic analog computer, the MONIAC[2].
[1] http://wiki.lspace.org/mediawiki/Glooper
[2] https://en.wikipedia.org/wiki/MONIAC