I agree with both of you on this, most certainly no Iran-Iraq war since Iraq had signed a reluctant territorial agreement in the late 70s, and only attacked because Iran was supposed to have been weakened by the revolution. Possibly no invasion of Afghanistan by the Soviets as well, since Iran was a powerful US ally in the area and they already had had some border incidents with the Sovs (that's what the F-14s were there for).
I'm not sure about the Gulf War, since Iraq would have remained a sworn enemy led by bad ole Hussein and his famously rational decisions
Bets are that he wouldn't have the temptation to invade Quwait with the full Iranian power (and US/NATO backing) looming over his head. A India/Pakistan-style local cold war with occasional clashes would make more sense.
As Marcello said, Hizbollah is another matter, since some opposition would certainly have sprung out in Lebanon. Remains to be decided why the revolution wouldn't have taken place. Would Khomeini and his gang still hang around somewhere? If so, with which kind of support? I guess he could end up in Lebanon to preach holy war against Israel much like he did from Tehran IRL and whip up a local Hezbollah-equivalent, maybe with opportunist support from Syria or some other neighbor. Turns out kind of like Bin Laden's story in reverse...
The strategical situation and motivations behind the Hezbollah's actions would be quite different of course.