I have a 63 Falcon convertible which has the exact same suspension as the 64 Stangs, and I was looking to lower it a bit. I just had the rear leafsprings replaced about 2 months ago and it came back a little higher than its supposed to look (too much space between the tire and the body). I was wondering if there is a DIY way to bring it down a tad myself, without having to send it back into a shop.

 

Sure is....buy mid eye leaf springs and spend an hour on the driveway installing them...should be a cake walk if you just had new leafs put in.
As for the front, take the coils out, and trim 1/4 coil of each or buy 1 inch drop springs

 

If you don't want to replace the rear springs they make a spacer block that goes between the rear end housing and the leaf springs. Most kits will come with longer u bolts. You will need them with the block. Most all of your internet mustang suppliers will have them.

 

the "spacer block" is called a lowering block and you can get them in 1,2, or 3" sizes.Most local parts stores will have them, cost about 20-30 bucks.