Reducing Noise Between Floors in Old Building

[Jesse Smith]

I own a 110yr old apartment building, with four symmetrical 2b/1ba units.  Two on the top floor and two on the bottom.

All units have beautiful, original hardwoods.  While lovely to look at, the floors do a terrible job dampening any sound from upstairs to down.  I've gotten complaints from my downstairs tenants that they can hear everything going on upstairs.

I've been reading about flooring options to deaden the noise transfer.  At this point, I'm planning to use an acoustic underlayment and install carpet in the bedrooms, at least.  

What products have you found to do the best job with this?  Any other ideas to reduce noise?  Wall treatments?