Coldwater Campground has three great Trailheads at the end of the Coldwater Campground road. So I would look there first.
Coldwater to Heart Lake: Easy to Moderate 2 mile round trip to Heart Lake. Follow signs to the Mammoth Consolidated Mine/Heart Lake on the left side of the parking lot. Mostly Brookies and some Rainbows present in Heart Lake. Take the self-guided tour through the Mammoth Consolidated Mine if you have time, well worth it.
Emerald Lake: Easy 1.5 mile round trip to Emerald Lake. Very scenic and popular trail. Not as steep as some, but still uphill as you follow a small creek. Be sure to take the right trail, as the Duck Pass trail also starts here. Brook trout can be found in Emerald Lake.
Duck Pass Trail to Arrowhead Lake: Moderate hike of 3.0 miles round trip to Arrowhead Lake on this busy trail. Expect Brookies and Rainbows.
Other Lakes for kids.
Crystal Lake: is a moderate 3.0 mile round trip. 650' elevation gain. Very picture perfect lunch spot. This is one of the more popular trails. Trail starts at the parking lot at Lake George. Look for the marker. Goldens in Crystal Lake.
T.J. Lake: Easy 2 mile round trip. Good hike for the kids. Trailhead starts at Lake George at the southernmost loop of the campground. TJ has Rainbows.
The Mammoth lake basin lakes get real busy during the summer and can get fished out in just a few days. When I took my kids fishing there we did best at Lake Mary over near Pine City Campground and George Lake to your left as come to the lake. Have fun and good luck!