I know that Minas Tirith is the White City. So what color was Osgiliath?
I'm making a terrain board of the ruins and have several destroyed buildings
and pieces to paint.
So, what colors would the majority of the city be?

It is pretty much exactly the same style. The cities were built by the same people at pretty much the same time. Their style and looks are very similar. Mostly white buildings are the way to go.

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Go The Glorf!
My W.I.P - viewtopic.php?f=50&t=28062

I see a lot of people painting the buildings white, when in the films it shows how much in disrepair the city was. the buildings have faded to a much more grey colour and there's foliage growing in and around them.
(i'd attach images but i can't figure out how)

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Isilduhrr has it right, Its just a dirty white/a light grey (use to be white), its pretty easy to paint (they ain't the multi coloured favela's! haha). Add your foliage and some greenery around the base and possibly some growing up the sides of some buildings for an interesting effect. With a simple white/grey lot of colours and some green basing materials you should be able to do a good job of it.

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Go The Glorf!
My W.I.P - viewtopic.php?f=50&t=28062

I like Dheneb Stone (I think that's what it was called) as a base colour for Osgiliath ruins.

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See my WIP thread here. viewtopic.php?f=50&t=25624

Here's what I do for the ruins.
1 Prime Black
2 Heavy dry brush of Rakarth Flesh(Dheneb Stone)
3 Light dry brush of white

Here's a battle report with some of my ruins on the table:
http://xinslair.blogspot.com/2013/02/my-first-lotr-sbg-game.html

Hope this helps.

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Xintao

Nice looking ruins.

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"the same as a duck you must be made of wood"