With a manageable distance and a perfect stopping point, this is a great route for families.
Eagle Mountain Lake Park has more than five miles of naturally surfaced, single-use (foot-traffic) trails. There is a pavilion with picnic tables, an informational display (ecology, flora fauna, etc.) area, restrooms, and water available near the main parking lot.
The Northwest Trail links the entrance to the Ridge Loop Trail, which features some fantastic views across one of the prettiest lakes in North Texas. The Northwest Trail is mostly wooded, but starts in grassland before descending towards the lake. It features a picnic area at its midpoint with a picnic table and restrooms.