Disc brakes would make the conversion easier, but 20" or 16" disc wheels are somewhat limited in choices.
I bought my SUNDEAL mini velo from Nashbar while they were on closeout for $275 and free shipping.
It's been 5 years since, I ride it occasionally when I need something light and easy to hop on and just ride away to the store.
8 spd, disc brakes, 20" BMX tires, not sure of the weight, but it's not heavier than a typical mt. bike.


Java Mini bike is a 16-spd, $650 on eBay purchase.
Has hydraulic disc brakes, very nice feel even with small 20" deep alloy aero wheels.