This can vary widely as this car was available with several different engine and transmission packages. Obviously a Mustang with the 170 cubic inch in-line 6 would not be as quick as a Mustang with a 289 4 barrel. The earlier models had a 260 V8, the later models had the more powerful 289.
The Mustang with the 289 4 barrel would go from 0 to 60 in about 7.5 seconds. Quarter mile in about 15.4 seconds @ 89 MPH.
In comparison the new 2012 Chevrolet Sonic economy car LTZ is just a tick slower. 0 to 60 in 7.8 seconds and quarter in 15.9. Not too shabby for something that will get you more than 40 MPG.
1964 Shelby Cobra 289 (288.5 cu in engine) 0-60 mph 5.8 Quarter Mile 13.7
This was the highest performance Mustang available in 1964. At the other end of the spectrum the 0-60 times for a Mustang with a 170 CID six cylinder with the A/C running is probably takes three or four times as much time to reach 60.
The 1964 came with the inline 6 cyl. and the 260 V8 . The 6 will probably be pretty slow but the 260 V8 if it has been rehabbed will probably get along pretty good , ya won't smoke a corvette but it will get over the real estate !