A quick check to determine if it's the exhaust pipe hitting the cross member is to see if it makes the noise more on an accelerating left turn, and less on a right turn. Turning left causes the engine to torque over more. Mine made sort of a clunk-clunk sound as the pipe banged the crossover - the harder the acceleration the harder the clunk.
To determine if the motor mount is shot on the passenger side, try to place your finger between the top heat shield of the mount and the base of the mount, the rubber should hold the mount sufficiently high to slip a finger in there easily. If the mount is good and the pipe is hitting there are two easy fixes to gain a bit of clerance; shim the crossover with three washers under the bolts on the passenger side, or loosen the exhaust manifold and the pipe mount at the tranny, jack up the exhasut pipe a bit, and retighten the manifold - but this might tear the manifold gasket, so proceed carefully if you try this approach. I found that the passenger mount sacks out in about 3 years, I guess due to the exhaust heat, even though it has a shield over it.
Those front flex discs are good for about 5 years too, but I have never had one make an audible sound, and I have trashed 3 so far on my '91 SE.