Wesley as a character (and Wheaton as an actor) was only slightly older than I was at the time, so for me he was a great character. He was smart and navigated relatively successfully in an adult world--or at least this is how 10 year old me saw him.
In hindsight though, I can understand why adults didn't like that character (or character type). Generally, the character type--ie any kid on an adult show from Wesley to Anakin Skywalker Ep. 1, to Nog and Jake Sisko--tend to be either too capable (Wesley, Anakin) or simply too distracting (Nog and Jake in mischief while DS9 is under real threats). I tend to think that especially in action/adventure shows, it is hard for adults to write for an average kid. In addition, simply due to limited experience, child actors tend to be less believable and realistic than adults who have had years of study and practice.
In hindsight though, I can understand why adults didn't like that character (or character type). Generally, the character type--ie any kid on an adult show from Wesley to Anakin Skywalker Ep. 1, to Nog and Jake Sisko--tend to be either too capable (Wesley, Anakin) or simply too distracting (Nog and Jake in mischief while DS9 is under real threats). I tend to think that especially in action/adventure shows, it is hard for adults to write for an average kid. In addition, simply due to limited experience, child actors tend to be less believable and realistic than adults who have had years of study and practice.