The car hasn't overheated yet or anything, and I don't notice any coolant leaks at all... but after running it for a while, and then turning it off, there is a gurgling sound coming from the coolant holding tank. There was recently a new radiator put in the vehicle (not by me), maybe air in the system?

1996 Dodge Neon
2.0 L
Automatic
180k

 

most likely air if your not overheating and boiling over.

keeep fingers crossed its not a blown headgasket pushing cylinder pressure into your cooling system.