Lover's Point, cove 3 (across from the Tinnery Restaurant) in Pacific Grove is one of the nicest shore dives in the Monterey area. The instructor that I DM for takes all of his open water students there. Easy to navigate, lots of things to see, not a million divers like Breakwater there every weekend.
Monastery is a great dive site, not someplace you want to go on your own until you've dove there with those who have before. I did 2 dives at South Monastery this past Saturday, easily had 60 feet vertical viz, logged over an hour bottom time on each dive. However, you have to know how to enter and exit the water properly. There were a few divers trying to enter the water in the middle of the beach on Saturday and they payed the price, tumbled around for quite a while until someone on the beach came and saved them. If there wasn't a big group on the beach watching these guys struggling, I would have had to go save them myself. Anyways, try Monastery, but go with someone experienced.
Mel