Hi Rachel: Because the hole will be in the floor anyway, I would suggest JT's advice of cutting the nail off flush with the floor (using a large set of side or end cutting plyers), and then 'set' the remaining nail below the surface of the floor. If you really want to get fancy, you can set the nail down 1" or more, then using a 1/2" forsner bit, cut a 1/2" or so deep hole and glue in a hardwood plug. This will work very well if you are going to have the floors sanded and refinished anyway. You will have lots of smooth, flush hardwood plugs showing, which is a feature of expensive hardwood floors.
If you just want to pull the nail and fill the hole, I'd think pretty hard about using a nail puller, unless JT knows of something new. I have both nail puller types, and I use them in rough framing nail extractions, as when you drive the mouth into the wood, it tends to leave a divot that would not look nice in a floor (smile). A simple oft overlooked method is to grab the end of the nail with a good pair of vice-grips (and use the Vice Grip brand) and gradually work it up and out without too much bending.