I have noticed my 2002 GMC Envoy (87,000 miles) loses RPM while idling at the stop light. The RPM jumps between 5000 and 10000 a few times while idle then rests at 5000. I notice this only happens when I come to a stop after driving on the highway. What could be the problem? Would it be solved by a basic tuneup?

SOURCE: 2004 GMC Envoy has trouble idling

Try the fuel filter. Sounds like the engine might be running rough due to weak fuel pressure. Its cheaper to replace, especially if it's still original from 04. Try running some injector cleaner through a couple of tanks of high octane gas.

SOURCE: ENVOY LOSES POWER AT HIGH SPEED

First thing I would do is replace the fuel filter. Could be clogging

SOURCE: What should the rpm be when idling?

depending on the motor, all makes and models should ranged no less then 500 rpm and 1500 rpm, the most common idle is about 1000 rpm and 1200rpm.

SOURCE: My 2002 GMC Envoy transmission slips into neutral

try adding fluid and if still slipping neeed to have it checked could just need a fluid change

SOURCE: GMC Envoy 2002. When I get to traffic stop light.

check your vaucumn hoses for leaks any leak in that system will effect your fuel pressure regulator and fuel rail that controls the running ability