No ground wire???

Those two outlets are most likely fed by BX cable. BX carries the ground on the outer sheath and enters the steel boxes. Get an outlet tester for a few bucks at Walmart. It has two leads black and red with a led on the end.. You stick them in the outlet and it will light up. Then stick the red lead into the right side and the black on the steel box and if it lights up then you have verified that the outlet is grounded. Now all you have to do is replace the old outlets. No rewiring would be necessary.

The metal jacket of the BX cable acts as a ground. Being in contact with the metal box, you can buy a "grounding wire", usually green with a threaded screw at one end, and screw that into the back of the box. Then buy your outlet of choice and hook the other end into the outlet ground terminal. Of coarse, if doing it yourself, don't forget to disconnect power to that circuit.

"Absolutely have an electrician run a new, dedicated line, or maybe two, just for audio. It usually cost less than $100, and is one of the best bang for the buck upgrades out there."

An electrician come out to you house and run 1 or 2 dedicated lines for less than $100.00? I would imagine the material alone would exceed that (depending on distance from panel box to audio outlets).

Using the BX shielding as your ground varies on building codes. The good thing is that if you have the shielding there and it's a home run to the box, you can ground it to the outlet on one end and the panel on the other. At a minimum consider using a GFI outlet in case this shield shorts somewhere...

As said above, if the metal box is grounded via the armor of the bx cable, you only need to install a "self-grounded" outlet. It will work without requiring the grounding pigtail attached to the box. A self-grounding outlet is a three-prong type that has a brass tab at one mounting hole that grips the mounting screw to guarantee ground contact. Even if the screw works loose, the outlet will still always be grounded to the box. No GFI necessary.

Self grounding receptacle:
http://www.cesco.com/resources/078477/572667-ProductImageURL.jpg

Grounding via yoke to box contact:
http://i171.photobucket.com/albums/u292/stickboy1375/graphic.jpg

Back in 1961 steel boxes were used for rough-in boxes along with 2 wire Romex. In this case the metal box would not be grounded. A quick look inside would reveal a Romex clamp with a screw in the middle of the clamp holding down the Romex in place. You should also see the outer sheath of the Romex extending into the box beyond the Romex clamp.

Steel box with Romex clamp.
http://www.zoro.com/i/G0645337/?utm_source=google_shopping&utm_medium=cpc&utm_campaign=Google_Shopping_Feed&kpid=G0645337&gclid=CP-xkKyevcICFcGPMgodHVIADg
.