I've lived & hiked here for 13 years and have never encountered a bear or mtn lion (or any 'vicious' animal). But I'm guessing that won't calm your fears. Any of the hikes on the plains should be predetor-free: they have no where to hide like the mtns. That said, snakes live everywhere (and I've encountered a small # on the plains) But you just keep the kids on the trail. You teach them. You be aware.
1. Teller Farm runs between east Arapaho and Isabelle Rd (aka Valmont) and continues across Isabelle to the White Rocks trail that is hilly, goes to the Heatherwood area of Boulder. Teller is flat, has cows sometimes. It's out east so you see the divide. It's wide so U could spot a snake from afar but I've never seen any there.
2. Waneka Lake in Lafayette is a lake loop with a small bird sanctuary, playgrounds & side fitness jobs. Wide, mellow, pretty. Not a hike but you can do laps for exercise.
3. The South Boulder Trail- you can pick it up off SoBo Rd, near 55th St. Goes all the way from almost broadway to ??? Baseline, Cherry Creek, etc. All flat, full of bikers & hikers, near the creek on & off. Well travelled = less wildlife, generally.
4. The Boulder Bike Path- paved, parallels Bldr Creek. Except it's a thrufare for bikers so you need to keep kiddo close, not wandering into the middle where a biker can come around the corner too fast. U can pick it up as far east as the Stazio Ball Fields near 55th & Arapaho and Eben G Fine Park at 1st & Arapaho. That park is a confluence of other trails, paved or not. But is also busy with kayakers/tubers in the summer.
5. Dry Creek trail off east Baseline (near the resevoir) is short, pretty, mellow.
Lastly, mtn lions are more active at dusk and brown bears (we have no fierce grizzlies) are moreso in spring. Carry a stick or pepper spray if that gives you comfort. I'm more afraid of jerky men than the wildlife here.
It's good to get the kids out in nature but also try to convey awareness not your fear to the kids. Good luck, have fun.