I was nine years old, but I already considered myself quite the old Trek hand; my father, while never involved in fandom, was a TOS early adopter who fell for the show in its original run, and after spawning, proceeded to pass the contagion on by taking me to all the TOS movies and sitting me in front of TOS reruns as soon as I could be relied upon to sit still.
I had all the Mego TMP figures and the TMP Read Along Adventure book-and-tape set, and I have vivid recollections of discovering the reruns of TAS on Nickelodeon, because, my god, here was all this extra Star Trek that I never knew existed! Suffice it to say, I was pretty far gone, and the bow of TNG was a major event in my household; I have unusually sharp memories of getting the issue of People that had a pre-release multi-page spread on the show, and I marveled at the huge cast and the strange uniforms and the bizarre-looking Enterprise.
I immediately took to Data and Geordi, my old buddy from Reading Rainbow, and the late '80s was not a golden age for live-action genre series, so TNG fulfilled my weirdness quotient.
On the whole, though, my reaction to that first season was not enthusiastic. I watched it regularly (because I was hardly going to not watch Star Trek, that would have been ridiculous), but I hated Wesley, I thought most of the stories were dull, I hated Wesley, I missed the constant action of TOS, and I thought Picard was a prattling milquetoast. I don't know if this happened a lot in multigenerational fan families, but there were many debates-bordering-on-arguments between my father and I that year about the merits of the show, and now that I think about it, my father was probably at his wit's end having to tolerate his child's constantly and loudly repeated conviction that Kirk made Picard look like a wuss, but he never showed it.
Over the next year or so, of course, the series became much stronger, and I relaxed in all my stances. The stories became tighter and more involving, Jean-Luc slowly won me over with his gravity and his seriousness, and I realized that my attitude toward Wesley was colored by a certain amount of jealousy (because that dorky kid getting to fly the Enterprise while this dorky kid could only sit by and watch was a baffling cosmic injustice). I was greatly amused when I started getting involved in online TV fandom in the mid-'90s and discovered that much of Fandom Assembled had the same criticisms of the early days that I did.