Fermilab is open to the public from dawn to dusk, however you must show a Real-ID compliant ID to enter the site.
The public areas include the trails around the lakes near the east entrance. Turn south at the stop sign in the village and park near the red barn. On the west side the trails around the prairie and Big Woods are open to the public. Park in the gravel area by the Margaret Pearson Trail. Map of public areas
See here for more information about public access.