When We install SCCM 2012 SP1 on Server 2012 

Why does it create the Microsoft Configuration Manager\AdminConsole\AdminUILog  folder in   in C:\Program Files(x86)

Shouldn't it just use normal Program Files as being x64 software

This is not created by the ConfigMgr 2012 installation. It is created by the installation of the ConfigMgr Admin Console which is a 32-bit application.

http://technet.microsoft.com/en-us/library/gg682088.aspx

Note that you do not have to install this on your server (it is an optional choice)

I installed 2 Site servers with similar settings.

On Windows 2012 sserver -- the AdminUi folder is on Program files x86

On Windows 2008 R2 -- It is on Program files

That is the reason i got a little confused.

The admin console is 32bit only, so it should be installed to Program Files x86. It might be possible that the environment variables on your 2008 R2 server are screwed or something like that.