8 is definitely old enough. I started taking my girls hiking when they were 4, and I try to get them out at least 6 or more times during each summer/fall. It's not always easy, but it's education. Adults take all this for granted, but just seeing a stream flow, some frogs in a pond, or a rock outcrop might make a child's day or summer. My daughter even though she is 5 will be able to tell you about every single deer that we have come across on every single trail from here to NY state. It's an entire wondrous world that they don't get daily exposure to (especially in flat-land/long Island)
I definitely agree with kayaker. Start them out easy. I take my girls around on hikes in NJ which are short (less than 3 or 4 miles) then I inch it up to the 5-6 mile range. Anything beyond that and it's just complaints the whole way. I'd say if you take them on 1 short hike each week for about a month, then they should be ready and able to take on a Catskill hike. I also have gotten in the habit of giving them a water bottle to carry for themselves, and a backpack to put it in. It makes them feel like they're hiking and carrying their weight, and they like stopping and taking breaks and rummaging through their backpacks.
I used to do North Point with my parents since I was 5, and hiked all over south mountain and mary's glen and escarpment and all that. So maybe I've got a skewed perspective. However remember we have 2 million years of evolution behind us, and this terrain is what we were built to traverse. It comes naturally. I would suggest Balsam
lake mountain fire tower (balsam mountain is a bit longer/more elevation gain) Windham highpeak is a fairly easy trail, but it is about 8 miles long. Also just to the south of Catskills is Shawangunk Range, which most of the hikes are lateral, and do not gain much in elevation but still have spectacular views.
There are plenty of smaller hikes and day hikes. I'd suggest Kaaterskill falls, but you might want to wait until after spring melt for that, as it is dangerous and people do die there from slipping into the torrent.
I have succeeded in taking the girls up to one 3500 peak. Windham highpeak is a long hike by comparison to the stuff we do in NJ but I convinced my wife and the girls to follow me up there. It definitely took some "cajoling" at 3500 feet to keep going. But it is definitely an experience that they won't soon forget.
The girls taking in the view of Blackhead Range from Windham High Peak
I say that getting kids exposed to nature is always a good thing. It doesn't matter for how long, or how much altitude you gain, but just do it. The more you do it the more accustomed they will get, and eventually they will get a "trail-foot" and be able to take on larger hikes.