I think my favorite gaming memory of all time would have to be entering the greater world of Gielinor in RuneScape on my second character. My first character was created back in 2004 as my dad was looking for games I could play to live out my Lord of the Rings obsession I had at that point but I didn't understand how the game worked and I ended up losing all of my "hard earned" loot (which constituted of some training gear and a few planks) when I decided to fight a level 7 farmer as a level 3 noob fresh off of Tutorial Island... but I digress, I didn't start to truly love the game until I gave it another chance two years later when I created my second account (and my main).
So yes, my favorite gaming memory is probably after I created that account and was unleashed into the game world. I still didn't fully understand how the game worked but I understood it a LOT more at that point as I actually paid attention to the tutorial. When I entered Lumbridge for the first time on that account, it was like I had truly entered an entirely new world. I was absolutely stoked to explore the game world, to immerse myself in a roleplaying experience that has only been matched by Bethesda's Elder Scrolls series (which I only got into thanks to RS).
Even trying to recall details about this particular memory is filling me with no small dose of beautiful nostalgia, I can still hear the tune of Harmony
playing as I explored the peaceful town of Lumbridge while I thought to myself, "This world is so beautiful.". I spent far too much time listening to the two organ tracks that played in the town's church. I spent time yelling at bots, demanding that they stop chopping the "sacred tree" behind said church which led to me making my first friend. I found myself admiring higher level players who passed through in their glistening armor or flowing magic robes. I eventually found my way to the desert town of Al-Kharid where I roleplayed as a prince (and got reported for impersonating the game's staff, which led to my mom making me play without chat for quite a while) but my Lumbridge memories will still always be my absolute favorite and most-cherished.
It's no exaggeration to say that RS has repeatedly changed my life across the 17 years I've been playing it but those memories were probably the first time that a video game truly made such an impact on my life. I will always love remembering them, no matter what.