I was late to the party, but bought it on March 24th, 2009 (the day Quantum of Solace came out on home video, which is how I'm able to bring up the specific date... I can just look up when QoS was released on DVD). I went to McDonalds while I was out and ate in, and remember eating my burger and fries while looking through the manual and getting more and more excited to play it. So I finally get home and start playing, and... wow. The graphics, physics and atmosphere just blew me away. It just felt so real - I'd been playing a lot of Saints Row 2 at the time, and I remember thinking "Jeez, this makes SR2 feel like playing with Lego". And yeah, I'd come to agree with some of the criticism about it being too repetitive (I don't agree anymore, mind you), but even if the game wouldn't really CLICK until my third playthrough (to the point where I have very little criticisms regarding the game and have embraced it wholeheartedly), I had a lot of fun on my first.
I specifically remember being surprised by the humor in the game; I'd heard so much about GTA IV being grey and depressing and 100% stone-faced and serious that I was pleasantly surprised to find it the funniest of the series (I still do!). And I found the story to be very involving, and instantly loved Niko. He's always been my favorite GTA protagonist.
As for weird memories... hmm. While I was doing the sniping portion of "Deconstruction for Beginners", I was enjoying a nice cold Snickers I'd put in the fridge, so I'll always associate that segment with Snickers bars And due to me getting McDonalds after getting the game and reading through the manual during my meal, I'll always associate the whole game with Mickey Ds. Which is appropriate I guess, seeing as how it has the biggest emphasis on fast food in the series. Oh, and for some reason, I thought Vlad was gonna be the main antagonist hounding you through the whole game, like a Tenpenny or Sonny. So when Niko shot him in the eye and caused an Old Faithful of blood to come geysering out, I was... pretty surprised And no, I didn't even suspect Dimitri. In fact, I actually remember reading one magazine article with a screenshot of Niko and Dimitri sitting on the bench, and the caption horribly mistook Dimitri for Roman! So before playing the game, I assumed Roman was gonna be this skinny well-dressed nerdy guy, and was kind of surprised when this tubby guy in a gaudy-ass shirt showed up, haha.