I think all the best suggestion have already been covered, but I'll put in my .02, anyway.
I GC with my wife and out two kids, a boy 3.75 years old and a girl 6.75 years old. They absolutely love the whole concept and get excited when we set out for a days worth of GCing. To them it is very much about the prizes in the cache, but also being competitive about who can find it first. More often than not one of the grownups finds the cache and then stands aside giving hints and suggestions to let the kids be the "superfinders."
We carry a backpack officially designated the "Geocaching bag." It contains the usual stuff like bug spray and first aid supplies for skinned knees and thorn-torn flesh, but we also throw in a good supply of granola bars and other snacks, plus a couple sports bottles of water. The kids get hungry and thirsty very easily and a fun GC can turn into an unfun experience with a three year old whining "I'm hungry..." every 15 seconds for half an hour.
In the GC bag we also put our items for trade. My wife used to sell tupperware, so we have loads of useful little doodads around from that (toothbrush holders, citrus peelers, mini product keychains, etc.) promotional items from the hospital we both work for (pens, digital thermometers, cap grippers, squeezy balls, etc.) and we regularly take trips to closeout stores and dollar stores to get other good things like extension cords, folding frisbees, flashlights, decks of cards, lip balm, etc. Depending on the quality of what comes out of a cache, we will trade evenly for it. If it is an especially good cache finding-wise, or one that obviously took lots of work (multi-caches) we will often drop in something of greater value as a 'thank you.'
The kids usually poop out earlier than the grownups during a day with 8 or more GCs planned. They don't recover as well from long hikes. We play it by ear. I usually plan out a route around an area with GCs in it, taking into consideration the difficulty and terrain rating, plus reading through logs to guage whether the kids would do well. I try to keep the round trip hike under a mile, if possible. They seem to enjoy more frequent and quicker finds. They also get easily diverted by playgrounds, which seem to be present at a lot of the parks where GCs get placed around here. After the find, we give them 15 or 20 minutes of swinging and sliding and seesawing. This makes them much more agreeable to more GCing.
One of the nicest things about GCing is that it's something healthy the entire family can do together. It can be as hard or easy as you like depending on your energy level and mood. I am in my mid 40s and have/had a lot of health problems in my life. It's only recently that I have gotten them dealt with well enough to attempt something like hiking, so GCing is hiking with a purpose. IT gets me out from behind my computer screen but still allows me to indulge my well-developed affection for gadgets. I started with a used Garmin Etrex LEgend and because of how much use it got, I justified a brand new Garmin GPSMAP 60cs this year.
Best of luck with your searching!
~daxe