Don't worry about it. Let it install into the Program Files(x86) folder. This is correct. Do not try and force it into the Program Files folder. The reason for this is because some 64bit application are actually only 32bit applications that are compatible with 64bit computers. Windows detects this and puts it in the x86 folder. This is all perfectly normal and iTunes should work perfectly on your computer. If you have any more problems, just post back.
Richard
EDIT: The only part of iTunes that is properly 64bit are the CD burning drivers.
1 x 640Gb (SATA 300)
Western Digital: WDC WD6400AAKS-75A7B0
1 x 1Tb (SATA 600)
Western Digital: Caviar Black, SATA 6GB/S, 64Mb cache, 8ms
Western Digital: WDC WD1002FAEX-00Z3A0 ATA Device
PSU
Stock PSU - 375W
Case
Dell XPS 420
Cooling
Stock Fan
Mouse
Advent Optical ADE-WG01 (colour change light up)
Keyboard
Dell Bluetooth
Internet Speed
120 kb/s
Other Info
ASUS USB 3.0 5Gbps/SATA 6Gbps - PCI-Express Combo Controller Card (U3S6)