There's a load of Celeron 1037U based boxes around too which are fairly cheap.

That Intel Atom Z3735F which is in the boxes Sinky mentioned is actually 64 bit.

And this

http://www.aliexpress.com/item/NEW-Fast-shipping-CS928-mini-PC-Intel-Atom-Z3735F-CPU-CS928-smart-computer-2GB-DDR3-16GB/32279884811.html

even at current exchange rates looks very cheap.