In general, the water is warmer and the viz is better in the Winter in Monterey. Yes. Wamer and better viz in Winter.
The warmest dives I have done in Monterey were November (57 degrees at depth). The coldest were May (47 degrees at depth). October dives were in the mid 50's, and August was in the low 50's.
The further south you go (in general) like towards Carmel and Pt Lobos, the colder it gets, and (in general) the better the diving is. However, there are some great spots right in Monterey for shore or boat diving.
I have only used the Monterey Express, and I have been very pleased. If holds about 20 divers (give or take) and you can sign up online. They do a good job, and they have taken us to a variety of spots.
I have heard good things about the Cypress Sea, but I have never used them. (it is on my list to be able to compare the two)
Breakwater is the most popular shore dive location. It is used by maybe 70% of the people that get certified in Monterey for the ocean dives. My instructor stays away from Breakwater because it is so crowded. However, there are some facilities there, two dive shops within walking distance and a lot of things to see. If you dive a little further out than the classes, you get a chance to dive with a LOT of sea lions.
There are several other shore dive locations, such as Lover's Cove that are real nice. However, the boats take you even better places.
As stated elsewhere, keep the "locals" informed about your plans, and some of us will try to join up with your group!
Just my opinions, and only because you asked.
Wristshot