If the problems came with the belt change, the shop messed with the CAS (camshaft angle) sensor and threw off the timing.. Seems to be happening a lot on the VG30DE/300ZX engines lately.. You do no have to even touch the unit..just remove the plug connector. Worse, the timing belt is off a tooth..or close to with wrong tensioner setting..or the apex pulleys (often overlooked) is on it's last legs. If the car went it fine, and came out wrong..you know where the problem lies. Don't take no for an answer..make poor mechanics and service writers pay.
If the timing belt has no relevance to the issue. You are going to be checking the MAF sensor and connectors.. You will be checking the twin throttle bodies and cleaning them thoroughly, along with the TPS sensor (calibrate it) You will be checking my ultimate suspicion. IAA-AAC unit..located behind the plenum.also known as idle control valve.. Check this page
http://www.twinturbo.net/ttnettech/iaa/iaa.html This is a notorious culprit on the VG30DE..usually overlooked.. However, what he does not mention is it can be cleaned of the soot in the chambers and you can test the wax mechanism in boiling hot water... Along with all of this, just check the Oxygen sensors and make sure they are performing like they should..they get lazy over time and need to be replaced..a basic tuneup if you must.. Check the fuel pressure circuit..faulty fuel pressure regulators can do this..measure it with a gauge hooked into the fuel lines... Post back with results..