I have the Furman unit you linked, and it is a very solidly constructed surge protector. It has a very nice rocker switch that is not going to accidentally be switched on/off, specially spaced outlets on the back for large AC adapters, and a convenient front outlet. It is also rack-mountable, which helped me to save space in my apartment.
But it's not going to fix ground loops or other sources of EMI. If you're having noise with absolutely nothing plugged into the amp (aside from power), then I would first make sure that your outlet is properly grounded; you can get an outlet tester for less than $10, e.g. http://www.amazon.com/Sperry-Instruments-GFI6302-Outlet-Tester/dp/B000RUL2UU
If the outlet is wired correctly, try removing all other electronics from the vicinity of the amp (or take the amp somewhere that has no other electronics). Turn off all your lights, computers, etc. and see if you still have the noise. If that gets rid of it, then your amp is picking up noise from the environment, so you should make sure only your amp (and other guitar gear) is plugged into that outlet, and keep other electronics as far away as possible. Putting ferrite chokes on power cords may help, but that is debatable.
If the noise persists, then the ground loop is within the amp itself, and you will probably need to take it to a technician (amp repair, NOT a guitar center-type store) to fix it.
If you get a 2 to 3 prong adapter, it will have a small loop of metal sticking out the bottom. You should connect this to ground, usually the easiest way is to attach it to the screw on the front of the fixture.
This may or may not provide a path to ground. Since two-prong outlets were typically wired with two-conductor cables (or knob and tube or whatever else), there was no ground wire brought into the box. In some scenarios, the box and the conduit that feeds it may serve as the ground all the way back to the panel, but if what's in the wall is just old two-conductor Romex (or the equivalent), then clipping that metal loop to the outlet isn't going to do much.
Some details here:
https://acworks.com/blogs/ac-works-connector/2-3-prong-adapter-and-outlet-safety
(Note: I don't know anything about local codes in NYC or anything about the history of electrical wiring in the city. It wouldn't surprise me at all to learn that the city has its own unique requirements or a history of using materials that aren't common in the rest of the country.)
By the way, you can test your outlets with one of these little testers:
It'll tell you everything you need to know about how an outlet is wired.