Having grown up in Monterey Bay and being a 'very' frequent guest at the aquarium (a MUST see btw) and having a Mom that is the manager of the Moss Landing branch of the Marine Mammal Center; I hope to shed light on a few things. There is nothing "illegal" perse about taking marine wildlife, with the exception of the protected species and areas. Please do some careful research, as a large portion of the Monterey Bay is currently protected, especially near the southern edge (Seaside, Marina, Pacific Grove).
Here are a couple links you need to start with. If you need anything else at all, or just want some more insight, please let me know.
Also, where abouts in Monterey Bay are you going?
http://www.dfg.ca.gov/mlpa/pdfs/ccmpas_brochure.pdf California Department of Fish & Game, Marine Life Protection Act Initiative
There is a huge support for the protection of the intertidal areas of the Bay (by some usually over-zealous folks with too much time on thier hands!) but it's enough to warrant caution.
Check up on the tidepool initiative. A group of activists started lobbying all the local governments (cities, counties, etc) trying to get them to totally ban the taking of everything. I don't think they got that far with their pleas, but I haven't lived in that area for years.
Anyway, great luck on your trip, have lots of fun, and make sure to go eat at Bubba Gump Shrimp - its just down the street from the aquarium.
PM me if you have any other q's