Port Royal Park is mainly a nice soccer field, usually filled by organized teams, plus a small children’s playground.
We find the park to also be a good starting point for a walk south along the San Francisco Bay Trail. First go a bit east to the left of a narrow canal, then go southwest along Belmont Slough towards Oracle Bridge. You can cross the bridge to get to Redwood Shores, or, you can keep heading on to the Belmont Conference Center & Sports Complex (you’ll see several baseball diamonds here). From the Sports Complex you can continue on via an overhead walking bridge across Hwy 101 to Ralston Ave in Belmont.
Another option starting from Port Royal Park is to head due west along a straight canal that will take you to more trails at the southern end of O’Neal Slough/Marina Lagoon.