To me, if it wasn't for San Andreas, there would be no Saint's Row, a franchise clearly modeled after the insane, unbelievably, over-the-top aspects of the life and times of CJ and his insane band of cohorts.
Actually Saints Row & Saints Row 2 were gang-related games with little over the top stuff, and SR3 and SRIV were over the top, aliens and zombies on steroids with f*ckin flying cars and sh*t with super-f*cking-hero protagonist.
For me, after SR2 the series went completely downhill.
But anyway now on topic:
My favorite aspect of the game was exploring, thus finding new ways to complete missions and progress the story or just causing complete mayhem
SR1 and 2 are very over the top, in a very real sense, like San Andreas is over the top.
I definitely agree with you, however, that it may not seem that way when compared to SRTT and SRIV, because those games are just insane. lol
But before SRTT, I looked to SR2 because it was a sort of "next gen San Andreas," where GTA IV was more grounded and realistic. When I say OTT in SR2, I am talking about two main components:
1. Where it is very similar to San Andreas. Things like gangs, factions, takerovers, the insane gunplay, all the wild unlocks and rewards, the ability to stand off against law enforcement and gangs (at the same time!) at full notoriety. Plus the ability to drive like a maniac and your cars keep traction, the planes and chopper races, taking over territories, the UFO, and a ton of other things that, in many ways remind me of San Andreas to this day.
2. SR2 actually took it up a notch in terms of insane gameplay. lol things like missions where you spray feces all over the city to devalue property while your AI allies chat about the most ludicrous things in your ear. Crib and automobile customizing is fantastic in that game, as is the huge plethora of personal customizing, abilities to choose your sex, voice, character, body type, features, makeup, and ethnicity and skin tone.
To be honest, even without SR3 and IV raising the bar on wild insanity, if you factor those games out and pretend they never existed, SR2 is pretty over the top! It just doesn't seem that way by comparison.
On topic: Totally with you about exploring San Andreas and finding new ways to beat the missions. One of the little challenges I like to do very early in the game is to stockpile ALL weapons I can before doing any missions after opening the Ganton crib. My little challenge is this: I break into the Los Santos airport and steal the Dodo, and fly it directly to the San Fierro Airport, a few feet away from where the homing RPG spawns. I then kill all the cops around and run to pick up the RPG and try to get back to my Dodo to take off and lose the automatic wanted level. Its not easy because not only are the cops firing, but the Hydras scramble and attack you. Then once I am in Red County, I either crash land on the grass and try to make my way over to the Pay 'n' Spray in Dilmore, or if I my Dodo is still in decent shape, I can usually fly it back to Ganton, land on the big circular driveway, and either run into my safehouse and save or land somewhere near another Pay 'n' Spray and steal a car to lose my wanted level.