I just posted this at work and it seems like not everyone knows this.
You can take the Amtrak Coast Starlight from Seattle, Portland, Sacramento, Oakland, San Jose or LA in the other direction, to the Monterey Bay aquarium. On Amtrak.com, simply put Monterey Bay Aquarium as your destination and when you arrive in Salinas station at 12:20pm (daily), there will be a bus that waits for you and picks you up to send you to the doors of the Aquarium by 1:30pm (usually takes just 20min)
For a true car-free experience, book a hotel room in New Monterey near the Aquarium, like the Clement Intercontinental, Monterey Plaza, or Wave Street Inn or anything on that side of the tunnel (including Pacific Grove). You can walk / bike the coastal trail.
Rent a bike from Work Horse bicycles downtown.
If you bring your own bike on the train (check in without boxing!) you can put it on MST city bus no 20, the bus station is 5 min ride away. Wait at and have a taco at Tacos Don Beto next door. There is a small outdoor area for Covid cautious folks.