Kids are fascinated by watching stuff grow and develop, be it plants, a pet, or their LEGO creation they are convinced will deserve accolades from all those privileged enough to witness. When it comes to a family garden, the biggest problem is stopping youngsters from raiding the produce while you are not looking. Many a time my offspring have returned from safari clutching a half munched cucumber, or sporting a rash from green tomatoes.
Whether you have a green thumb, or like Dad U, are the Infrastructure Guy*, garden projects can be tailored to fit any point of the family interest/scale/budget. From a potted plant on the balcony, to veggies in planters and pots, or a dedicated plot in the back yard, involvement in the setting garden can bring delight to little kids. Despite occasional groans about weeding from the chore-laden older set, all is forgotten when that first tomato ripens. Consult someone who actually knows what they are doing** before initiating a project into uncharted territory. Be patient and wait out the “last frost” in Spring which can obliterate seedlings, but can come weeks after daytime weather has become too perfect to resist. Local garden/hardware stores will have all the info you need to select the range of veggies you could expect success with, as well as options for fertilizing and bug control (which range from organic co-planting plans, to the possibly somewhat less healthy but far less finicky “nuke-em” strategy).
Dad U recommends blueberries as a particularly easy crop to manage if your local conditions support it. In my case, no actual picking was personally required for at least the first 5 years. Only after that point was I informed that we had been experiencing yearly bumper crops, but my plague of locusts had been stripping off all the ripe berries while I was at work.
*Competent to make garden beds, shift dirt and manure, hammer stakes, build fences, and repair garden hose fittings, et al, but has the unfortunate ability to kill actual plants just by feigning interest in them.
**ie, not an Infrastructure Guy
-get them outside