These aren't special event days — it's a standing weekly program, which means you can actually plan around it without watching a ticketing window. The de Young's permanent collection covers American art and art of the Pacific and Africa; the Legion runs European painting and sculpture with a deep Rodin collection. Neither museum is the same experience twice if there's a rotating exhibition up, and both usually have at least one temporary show running.
Practical notes: for the de Young, the Music Concourse garage underneath the museum is your best parking bet on Saturdays — $3.50/hour, validated at the museum for a discount. For the Legion, street parking on Clement or in the lot off 34th is usually manageable outside of rare event days. BART doesn't reach either directly — the N-Judah gets you close to the de Young (9th and Irving, then a walk through the park); the 18 bus runs to the Legion.
If you only have two hours, pick one and don't try to do both in a day. The Legion's location alone — clifftop, looking out toward Marin — is worth the trip even before you go inside.

