I tend to gravitate to the Presidio's west side more often for hikes, but the east and middle definitely have their charms too. For instance, to enter the park via the Broadway trailhead near the Lyon stairway is a real treat, and the Simonds Loop steps are also on the extreme east side.
From the Lovers Lane trailhead into the park, you can wind along the Mountain Lake Trail on the south side a short distance until you reach the newly renovated El Polin Spring picnic area and then up to Inspiration Point Overlook. This time stepped down from Lovers Lane after a few yards onto a favorite sandy trail that's just below the Mountain Lake Trail, across from the beginning of the Wood Line forest sculpture.
Meandered along to the west in the thick sand and warm sunshine and along a trail that during blackberry season provides good yields. Soon was looking out over El Polin from a trail above. A couple of ducks were diving in the northernmost pond when I got down there. There's the old stairway down and a longer, steeper one up the west slope that will take you to the Ecology Trail which curves around to Inspiration Point Overlook. First pic: a view from above, showing the older, shorter stairway down from the south slope.
For a change, however, headed north through the residential area where I discovered yet another new neighborhood garden in a space between homes near El Polin on McArthur near Wallen (second pic). Went up a few steps from Wallen (just because I'd always only passed by it before without ascending). But there was no real trail there, just pine needles and tall grasses; it was short and then I was on Quarry Road, the next residential street up. At Quarry and Barnard are 36 steps to Moraga at the Main Post and the newly opened Inn at the Presidio. There's now a plaque on the front: "Historic Homes of America. National Trust for Historic Preservation."
You can continue west straight through the Main Post to the steps that lead up to the Post Chapel. Detoured this time to the temporary Visitor Center (just past the Disney Museum), but found it closed (hours: Thursday-Sunday, 10 to 4).
Headed back uphill (aromas of freshly cut grass and eucalyptus) towards the front of the Post Chapel (love the architecture; third pic) and round to one of my favorite trails. This one zigs and climbs through sun-dappled, birdsong-y woods at the south side of the cemetery up to the Cemetery Overlook. In the distance the Bridge was mostly blanketed in fog (fourth pic). The Overlook steps (98 or so, fifth foto) will take you back into the forest again and down to the Park Trail.
At the top of the golf course, continued south downhill to the Mountain Lake Trail (also an excellent area during berrytime). This trail takes you under a highway overpass and around Mountain Lake (a groupwalk and several redtail hawks seen).
If you exit the park here, you can walk all the way south to Golden Gate Park on the island trail that divides Park Presidio. You do have to cross each of the E-W streets, but then can get back on the greenway. This time just went from the park to the bus stop on California.