I can show you plenty of hardware that is perfectly 64 bit capable but probably never will run Ubuntu and/or Unity.
First, what is 64 bit for you? Looking at ubuntu.com/download and getting images from there, one gets the impression, that 64 bit is amd64 (also called x86_64). If one digs deeper to cdimage.ubuntu.com, one will find non-Intel images too: PowerPC and amrhf. As the PowerPC images are said to boot on G3 and G4 PowerPCs, these are 32 bit. Armhf is 32 bit too (arm64/aarch64 support in Linux is just evolving). So yes, if 64 bit means amd64, I do have hardware that can run Unity.
But you asked if I have hardware that is 64 bit capable and can run Ubuntu/Unity, so may I apply my definiton of 64 bit here? I have an old Sun Netra T1-200 (500MHz UltraSPARC IIe) running Debian's sparc port, which has a 64 bit kernel and 32 bit userland. Unity? No wai.
Sorry for ranting like this, but 64 bit really just means that the CPU can handle 64 bit big addresses etc. End even then, it not always will do so ;)