All good suggestions so far. I would add
1) fish tacos at Turtle Bay Taqueria in downtown Monterey
2) Plumes coffee house, also downtown Monterey
3) the Old Town Monterey farmer's market if you happen to be there on a Tuesday
4) Nepenthe, a restaurant with a spectacular location on the ocean side of Hwy 1 in Big Sur - very casual with lots of outdoor seating; one of the most beautiful spots you will ever see
5) watching the surfers in Santa Cruz, either at Steamers Lane near the West Cliff lighthouse, or the Pleasure Point/the Hook area further south.
Often there's big surf at this time of year, and only 45 minutes from Monterey. Free.
As previous posters have said, the aquarium is not overrated, it's not to be missed. Also Asilomar and Carmel beaches are beyond beautiful.