I'd start with the idle control solenoid. Sticks right out front above the coolant hose. Pull the plug off and see if you have 12V. If you do, cycle the plug a few times, you should feel the solenoid "vibrating".

If no 12V and no "vibration", there is a control box behind the glovebox that controls the idle speed. If it fails (usually cracked solder joints), the default is to run high idle (1500-2000 RPM).

__________________
Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]