Begin at the trailhead across from the parking area. The initial trail (Alpine Trail) is a steep step up with railroad ties to prevent erosion, but the trail afterwards is generally well graded. Almost immediately, the trail intersects with another. If you turn right, the trail narrows and will eventually become a single-track trail suitable only for carriers or backpacks. If you do not turn right, the trail remains wide and is suitable for a baby jogger or other large-wheeled stroller, though there will be some rolling hills to push that stroller up!
Continuing straight from the trailhead, you’ll ascend some rolling hills to eventually get to the highest parts of the open space. Old Spanish Trail is largely shaded and winds up and down rolling hills. It will cross Bay Laurel Trail, a nice, but short trail, that would be fun to take with a jogging stroller if Arroyo Trail the subsequent trail needed to stay in the park (versus going to neighborhoods) were not so narrow and steep in places. Stay on Old Spanish Trail until you reach Fire Road Trail, a quite obvious fire road, near where Arroyo Trail and Coal Mine Trail cross. You can follow the fire road or hop onto Coal Mine Trail for a short distance, continuing SSE, passing a water tower.
Old Spanish Trail will continue from the fire road, to intersect with Lake Trail, which is the one to take to the right to get to Alpine Road. Once at the road, turn right and return along the smooth, paved, Alpine Road (just watch out for residents driving the road), with views of the creek generally to your left.