Carmel Valley definitely gets more sunshine than the others. Pacific Grove probably gets the most fog and coldest weather. I recall reading that's because some methodist sect clear-cut it in the 1800s so they could have a larger campground during the summer. For some reason the lack of tree coverage leads to more fog.
We came very close to buying in Monterey near Monte Vista school in 2020. View of the bay, close enough to walk downtown but far enough to be out of the traffic and the touristy areas. We put in the highest offer, all cash, above asking, and were told after the offer deadline passed by the seller's agent that "the house was ours." Unfortunately the seller's agent and I later learned that the seller had allowed someone to see the property after showings were over, and that the wife met the family, which was "a mirror image of their own" "and she fell in love." Ugh. Long story short, the seller took less money just because the wanna-be buyers had a child the same age and with the same fucking strawberry blonde hair as their own. It was heartbreaking at the time. We had spent 6 weeks looking at houses and that was the only place we found within that span worth putting an offer on. Three days later we had to head home because the pandemic was kicking off in the US.
PG can be pretty boring, restaurant and entertainment wise. I love the walk/jogging path along Asilomar Trail. Just a total privilege to be able to walk out of your house and take that loop along the oceanside. This is just something someone once told me - PG is built on a rock and the theory is it's the most earthquake resistant area up there.
There's a particular neighborhood in Monterey to avoid due to fire danger and insurance issues. If memory serves, it's called Skyline Forest area.
There's more restaurant choices and culture over in Carmel, and it's much easier to get to Point Lobos. Obviously more tourists to deal with but the beach area is also leash-free for dogs, so that may be important if you're a dog person. I'd guess Carmel Valley also has fire risk issues. (Pacific Grove has an unofficial, illegal dog beach area when the tide is low and so is the tourist season.)
I think it's hard to go wrong either way you choose. All things being equal I'd pick Carmel by the Sea or Pebble Beach, but so much depends on what's available on the market.
Possibly worth noting - the local hospital is "Monterey Community Hospital" or something but it's now owned by private equity. A lot of people make the drive into Salinas for healthcare. Doctors seems to not stay long at the Monterey hospital.
There's a woman in Monterey, Julie at Bliss Bodywork, who may be the best masseuse ever. I'm not embellishing in the least.
Oh another point for PG is the TJ's is far less busy than the store in downtown Monterey.