Monterey has the ocean/bay on one side and mountains (technically, more like hills) on the other, so it is hard to carve out a good ride with elevation since there are not many roads in the hills. No rolling hills, it is either flat or a climb.
The rec trail south of Fisherman's Wharf in Monterey is too congested with tourists and I would not recommend riding it unless you go really early or ride slow. North of the wharf is fine. The entire rec trail/17 Mile Drive is pretty flat. Traffic in Monterey is pretty calm, so I would not worry about riding in the road except for a few specific places.
I really like budkid's suggestion for Carmel Valley and over Laureles Grade:
Bike Ride Profile | Laureles Grade...you always kick my butt. near Carmel | Times and Records | Strava
The climbs here are not long and "the grade" is probably one of the hardest (still not that hard). There is no shoulder on the upper half, so you need to be careful. Getting to Carmel Valley Road can be problematic depending on where you start from since you can't ride down Highway 1. Extremey annoying.
Another good climb is Jack's Peak. Here is a recent ride where I went up Jack's Peak and Veteran's Park:
Bike Ride Profile | Forgot my water bottle, took it easy near Monterey | Times and Records | Strava
Fort Ord is great for biking since it is closed to vehicles. There are a few roads you can take. Here are some of the ones I do:
Bike Ride Profile | Lunch Ride near Monterey | Times and Records | Strava
Bike Ride Profile | Lunch Ride near Monterey | Times and Records | Strava
Most riders actually start out near the entrances on Gigling Rd/Eight Ave or Normandy Rd/Parker Flats (both in the northeast corner). You might pass the occasional employee driving, but if not, open roads. The climb to do is Barloy Canyon up to Laguna Seca:
Strava Segment | Barloy Cyn from Eucalyptus to Summit. Black Death is another, but it is an out-n-back climb since you cannot bike after a certain point (dirt roads):
Strava Segment | Black Death Climb
Strava Segment | Black Death