Last year, we started renting bikes from Adventures by the Sea with our 4 year old and It's now become our favorite thing to do in Monterey. We've rented tag-alongs and biked to Asilomar or done the 4 person surrey and barely made it to Lover's Point. All of it is fun. They also have baby carrier attachments if you've some little babes to bring along too.
Highly recommend going in the springtime close to Mother's Day to see all the beautiful pink wildflowers (see pictures).
Monterey is often cloudy in the morning and then the sun breaks through in the afternoon. We usually like to do a ride in the morning when it's less crowded, get lunch and then head over to the aquarium after the morning rush and a bunch of the younger kids head home for naps.
The staff at the bike shop are really friendly. Give yourself about 15-20 minutes to get through the renting process though.
Rent a four-person surrey bike and cruise up and down the waterfront trail. You canalso rent surfboards, Segways, regular bikes, and tandem kayaks (kids 5 and up; child-sized life jackets provided) to paddle around the quiet parts of the bay to see otters, harbor seals, and kelp forests up close. Ask about tours that include instruction and marine life narration.