Hi, Computo!
Now (as Ross Perot would say), I live two hours from Monterey, have a bother, whom I visit often, who lives 20 minutes from Monterey--and I have never dived there! But I have gone there a lot, seen and talked to divers there a lot, and know people in the local (San Rafael) dive club who go there fairly often. So, in case no one of that bunch answers you, consider my thoughts.
Dive shops: The Bamboo Reef in Monterey is tops from what I hear--I think they do both boat and shore dives.
Marin Skin Divers in San Rafael has regular trips to Monterey--I think they also do both boat and shore dives.
You can do unguided shore dives by renting tanks at the Bamboo Reef and they will tell you where to enter. But, I bet it is easy to get lost in that murksy stuff. One place I have seen folks enter fairly often is at Lovers' Point--you might even see a wedding taking place. People also enter regularly near Cannery Row. There is a big parking lot that diver use--the best address I can give is 32 Cannery Row, the location of Backscatter, an U/W camera shop.
The reasons we do not dive Monterey are threefold:
(1) Cold water
(2) Murky water
(3) Kelp--entangling kelp
(4) Did I mention cold, murky water?
But there are lots of avid divers who are willing to don 7mm wetsuits, hoods, gloves, vests, lots and lots of weights, etc., and see the wonders. Myself, I go the Monterey Aquarium--which I recommend you do--dive or not.
Do you Kayak? If so, you can rent a Kayak and see the sea otters up close and personal--and breath deeply of the fragrance of sea lion feces as you round one corner of the bay!
Also, try the Old Bathhouse for lunch or dinner--pricey, but excellent food. For a place a little lower on the price scale, try Rappas on Fisherman's Wharf--good local sea food. And do not fail to try lots of our San Francisco Sour Dough French Bread! In fact, buy some sour dough, a good bottle of California wine and some Monterey Jack Cheese and drive down to Pacific Grove (adjacent to Monterey) along the shore and have a picnic while you watch the beautiful Pacific waves crash on the rocky coast! Very pretty!
I do not have the phone numbers of the places above handy, but if you want them, let me know and I will get them for you.
Have a blast!
Joewr