Our absolutely favorite Big Sur hike is the Bluffs and Panorama Trail via Creamery Meadow in Andrew Molera State Park. It offers sweeping views of the coast and access to a little hidden purple sand beach. Check out the AllTrails site for more details and directions.
This is hands down the best aquarium that we have ever been to and is definitely worth a visit if you have the time. The sea otter exhibit is a personal favorite.
Kayaks are available for rental in the Monterey Bay harbor. You are pretty much guaranteed to see some otters if you paddle around the boats. This company also offers kayak rentals at Elkhorn Slough Estuarine Reserve, which is protected wetland about a 30 minute drive north of the city featuring sea otters, seals and birds.
Point Lobos State Reserve is a 20 minute drive from the town of Monterey. It offers beautiful views of the coast, lots of wildlife sighting potential, and is a very manageable walk for people of all abilities. Their parking lot does fill up fast though, so it is best to either get there early and plan to pay $10 or park along the highway and prepare to walk a bit.