As divemas said, conditions have to be spot on to consider diving Monastery - it is a very tricky beach, especially when exiting. The beach is a coarse 2-3mm gravel rather than sand, and the waters edge is usually a dropoff into about 6' of water less than 10' from the edge, so waves tend to dump straight onto the beach. Kelp also extends right to the edge of the beach. If there is more than a foot of surf, you're going to be in for a rough time getting out.
All that said, there are two sites at Monastery - north and south. The south end generally offers the easier entry. Between them is lots and lots of sand, or gravel. The south end is a shallow 30' dive in and around rocks, covered in lots of soft sealife, but few fish. It can be very surgy in amongst the rocks, but because of the shallows, is very bright and colorful especially if the sun is out. A pleasant dive, and it's not unusual to encounter the more shy harbour seals during the dive. There are some sea urchins about here, so be careful if there's surge. Enter the water directly in front of the kelp, and take a bearing out through the middle of the kelp beds. Once you reach your turn pressure, a reciprocal course should bring you straight back to the beach. I like to head out away from the beach, and then make a left turn once I'm several hundred feet out, just to penetrate amongst the rocks a bit more. I don't have compass bearings on hand, but it's easy to find the beach by reversing course if you take a turn, and you'll hit sand - follow the border of rocks and sand to the RIGHT back to the beach. The kelp also ends at the rock / sand border. If you normally dive thirds amongst kelp, it's not required here - it's an easy escape to the sand by heading north, and the kelp beds have a distinct edge, so there's no worry about having to do the kelp crawl back to the beach.
The north end is the advanced end - it's easy to end up deep and narc'd here if you're not careful. Enter the water on the left of the kelp bed, and surface swim out part way along it's length towards the washrock (can't miss it). Drop down, and follow the edge of the kelp out, and you can see the Monterey Canyon first hand. The bottom abruptly drops away at a 45 degree angle - make sure you're not over sand when you hit this drop, because the sand just slopes down, and is very disorienting - you'll feel like you're sliding down the side of a houseroof it's that steep. Head north and you'll hit a boulder field tumbling down to the depths. Lots of big fish like lingcod and rockfish in here, crabs, anemones, if you can find it in Monterey / Carmel, you can probably find it here. The DEPTH is what you have to watch here though - the bottom just drops off into the black abyss, quite literally. It's not a wall dive as such, but just a sloping mass of ledges and boulders getting darker and deeper. I've been to 118' here before, before turning back, and I think 600' is not much more than a short swim away, before dropping down into the thousands. It's a bit spooky down there! Not surprised there's big sharks about. There is a washrock on the edge of the dropoff, so be careful when ascending the slope if you venture down it - it's easy to find yourself continuing up the washrock to 20' or less (did it once), and then having a 50' bottom for a long way back into the beach. Take a big light, your bestest most trustful buddy, and a conservative dive plan if checking this site out.
PS Watch out for wasps in the trees on the north end of the beack - I've got a scar on my arm from one of the little buggers. They didn't appreciate me taking a surface interval on their bush!
Oh yeah, and this site is more Carmel than Monterey, so if you're doing multiple dives here, bring tanks for each dive to save driving back into Monterey.