There are a few options for playing with a 16-bit 6502 like the Apple IIGS or the SNES.
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Or you could buy Western Design's 'Mensch computer', a full computer built around a variant of the 65c816:
http://www.westerndesigncenter.com/wdc/Mensch_Computer.cfm
Or you could buy a single board machine from them, through Mouser.
Or just buy a 65c816 and breadboard it. The chip is still made and available through Mouser. And can be clocked up to 20mhz.
There's also the 65C02 from Western Design.
OP was talking specifically about 16-bit 6502 variant