My 350 (Quadrajet) hesitates badly at a certain
throttle position - just a little above idle.
Sometimes it stalls if I keep it at that position.
Give it more throttle and it takes off and it
idles fine. Any ideas? Thanks.

Sounds like your butterflies may be open a bit too much.. causing a lean condition and starving the engine. Pop the hood and rev the motor by hand til it starts to falter.. put your hand over the venturi and see if she mellows back out.. if so, you've found the problem but need to correct it.

lol ****can that carb get a holley and be done with it lol.
without any info on the year car and make its hard to diagnose.
quads has a computer controlled carb and then they had the old regular quad that just ran great without the emissions etc.

Make sure you don't have any vacuum leaks like from the brake booster fitting on the back or PCV port. IMHO, QuadraJet is a fine carb as is Holley. People just like what they are used to. The spread-bore design of the QuadraJet is hard to beat if you get it set up right. But look for the vacuum leak before getting too crazy with carb adjustments.

As with other good suggestions given, with the engine off and air cleaner removed, view the air horn of the carb. Move the throttle, for every slight movement of the throttle, the accellerator pump should dispense fuel into the air horn.

This usually can be fixed with acc pump linkage adjustment. If the linkage is in the inner hole of acc arm lever, moveing it to the outside hole will help.