I'd say the 2000s to early 2010s. I didn't grow up with the NES but I did grew up with the SNES, about four after the SNES life cycle ended. While I enjoyed the 64, SNES, and a little of Game Boy, the 2000s to early 2010s were really the time my life as a Nintendo fan was prosperous (and in a way still is). From Melee to Prime, Wind Waker to Twilight Princess, Super Mario Advance to Pokemon Ruby/Fire Red, Pokemon Heart Gold to Y, Galaxy to 3D World, Brawl to Smash 4, Last Story to Fire Emblem Awakening, Animal Crossing to Splatoon, Wii Sports to DKCR, etc. I loved my GameCube, GBA, DS, Wii, 3DS, and even Wii U despite only having it for less than a year. Then you got third parties like Shin Megami Tensei IV, the Ace Attorney series, the Professor Layton series, Time Hallow, TWEWY, the Dragon Quest series, the Monster Hunter series, Red Steel 2, No More Heroes, Bayonetta 1 and 2, Soul Calibur 2, Tatsunoko vs. Capcom, etc.
All in all, while some will put the 90s and 80s over the 00s and 10s, the latter two decades (with the 2010s not even over yet) are nothing to scoff about. A variety of new ways to play, new unique series from different genres, revivals, remakes, and many more.