I test rode this Softail Slim S at my dealership. It was beautiful. It was also the shortest one I've ever sat on. I'd try sitting on one of these if you can find one.
Softail Slim S

 

best I can do is say go and sit test as many bikes as you can. there are seats that can help adapt for shorter riders. Worst case, you can always go with a trike. no need to flat foot one of those. Good luck

 

Aftermarket stuff; shorter rear shocks, forwards seats and pull back risers all combined will put you in a comfortable position for the controls and balance. Look at Low-rider dynas, Fat Boy softails and Road Kings as low center of gravity bikes
Is it possible? Yes.
Shortest one I know is a feller we call Little Man, he's 5 foot,, well maybe shorter now,, he's been riding for 40+yrs

 

 

 

 

The better half is 5' 0" with her hair proofed up (28" inseam) and is now on a 16 RG. She started on a sportster, spent a few years on a couple of fat boy lo (including 7000+ mile round trip to Sturgis twice) but always wanted a big bike. Like others have said the inseam is more important than overall height. 4" might as well be a mile, but something can likely be done. The slim or an 883 lo may be the answer. We tried every combination possible of seats, boots, and air ride and she's finally at a point where she's comfortable, safe, and the bike rides without clearance/suspension issues. One important thing is our dealer was very willing to find a way to make it happen other than just slamming the bike and killing the ride quality. Feel free to shoot me a PM, glad to help you out any way we can.

 

The 1977 onward Low Rider used to advertise a 26-inch ride height, so it is all relevant to what you want to spend.

http://dudeworld.com.au/ARTILOWRIDER.HTML

 

Look into a Ridley Motorcycle. They have very low seat heights, automatic transmissions and look very much like a Harley. My wife is 5'1 and she was looking at one several years ago. She sat on it and loved being able to flat foot it.