You will almost definitely see sea lions at the Breakwater if you swim out far enough. Doing a long surface swim at the beginning of the dive is beneficial in terms of how far out along the Breakwater you can get. The further out you get, the more encounters you will have. Sea lions will often actively seek you out if they see your bubbles - so hang around at around 40', and if you can hear them up on the surface (you can hear them barking even at that depth), more likely than not a couple will come down for a play.
Harbour seals are more shy, and will not normally seek out diver contact. I've seen them at Monastery Beach South. They tend to give you the once over, and keep a wary eye on you.
Leopard sharks - I've only seen them in Carmel at Pebble Beach, but there's quite a few sites I didn't get to do in Monterey that might hold them (like Pt Lobos).
How many dives do you have, and what are your surf entry/exit skills like? Monastery Beach (both north and south - north is the deep end) can be very unforgiving - there was a near-drowning there only a few months back (resulted in ongoing coma according to the last reports) that occured on exit - you will *almost always* have to crawl out on hands and knees to avoid being knocked down in the surf. No shame in it - might look funny, but it's the intelligent thing to do. The beach bottom curves upwards where the waves break in most places, and the difference between being chest deep, and high and dry, is sometimes only a few feet - so put your reg in your mouth, deflate your BC, and CRAWL out of the surf until you're up past the waves - even if they look small they will still knock you on your butt at the end of a long deep dive when you're wearing all that gear. Play it safe, and treat it like climbing back into a boat - keep your reg in your mouth until you're out.
The actual deep dive itself is not the danger, but be aware that you may encounter narcosis - just plan your max depth before your dive, and stick to it! I get narc'd on this site, and I had a buddy try to encourage me beyond 120' at this site, even though we'd agreed to that as a hard and fast limit. He was narc'd, and just wanted to go "a little deeper".
Keep an eye out under the big boulders on the slope - lots of big ling cod hang out there. Spend lots of time shallow to offgas your deep dive - check out the kelp bed on the way back in, there's some interesting stuff in there. Here's a profile of my last dive there in early August (we swam out almost to the washrock, dropped down to 100', worked our way back up the slope, then spent time in the kelp). Super dive.
