Your computer probably is able to be upgraded to Vista 64 but with so many caveats that you might want to rethink your desire to do so.
First, you will need to obtain the appropriate 64-bit drivers for all of your hardware and peripherals. In some cases, if any of your stuff is more than about five years old (and in some cases even younger), this might become complicated and you might need to spend some time seeking out third-party support (believe it or not, there are geeks out there who, just for pleasure, write new 64-bit drivers for "legacy" peripherals).
Second, you will need to do a complete wipe-and-load, of course after saving all your data to some form of external backup media.
Third, you will have to reinstall and reconfigure ALL of your software applications, and some of those may require updates that you will have to pay (again) for.
All this will get you very little benefit over Vista 32-bit, a very unjustly maligned but extremely reliable and capable O/S. Indeed, the similarities between 7 and Vista are so minor that 7 should have been released as a Vista service pack, in my opinion.
I'd wait before I go to 7/64 until I need a new PC if I were you.