I can't speak for a 2001, but on my 1998 I removed them through the trunk. Pretty quick and easy that way, just a few screws in each.
*Edit*
The 2001 Altima GXE Special Edition The way that I had to go about accessing the rear speaker housing was through the back seats.
I actually am going to be replacing mine tomorrow, and taking a tutorial video on how to replace them. watch YouTube.com/ohnoesitsroy for the video to be uploaded in the next few days.
Try to use the Nissan speaker adapters plugs so you don't need to cut wires and mess up the electric system, you can get those from eBay or amazon.
u have to remove the rear deck lid, speakers r underneath how do you remove the rear deck lid on the 2005 Nissan altima
You need to remove the rear seat, then remove the package tray.
I recommend going Crutchfield.com as they have instructions on how to install speakers in most cars.
How to remove the front bumper to a 1998 Nissan Altima?
Yahoo search 04 Nissan altima speaker and a you-tube link should pop up. 02 and 04 have the same set up so this should work for you vehicle
how to remove a power steering pulley on a 1997 Nissan altima
Remove the bottom backseat, you should see it there.
how to open dash on nissan Altima 2008
how to replace a heater core on a 2003 Nissan Altima 2.5
Should be located at bottom or rear of radiator or remove lower radiator hose
how to change a ignition switch on a nissan altima 2003
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