You should be good for PCH in June roadwise. The big spot now is at Mill Creek. Probably another month to clear it.

You will have fog though. And it'll be cool. Expect mid 60s during the days, 40s/50s at night.
For Monterey:
Past the aquarium as you go into PG, there is a seal haul out. Ocean View Dr just before 1st st.

I love Lovers Point. It's over in PG.
Keep driving west past Lovers Point and go to Asilomar for sunset.

Hiking, I like:
Huckleberry Hill (
https://www.alltrails.com/explore/trail/us/california/huckleberry-hill-loop-trail)Spanish Bay Trail (
https://www.alltrails.com/explore/trail/us/california/spanish-bay-trail--2)For Big Sur:
I think south is right, just because there is a view about 10-15 minutes south of Carmel that I love. Around China Lookout.


Point Lobos is nice, but can get crowded. California state parks charge by the car, so you will see a lot of cars parked on 1 and they walk in.
In the town of Big Sur, there is a bus in front of the River Inn that serves ice cream. Get some ice cream, then go down to the Big Sur River behind the inn and let the kids play in the river.
McWay Falls is a must. Since the state charges per car, most people park on Highway 1 and walk.
For reference, here's a pic of our car parked so we can walk to the falls.


McWay Falls
Beaches, I like sand dollar best. It's a good 1.5 hours south of Carmel. Pfeiffer is popular and has a cool arch and purple sand.

Sand Dollar

Pfeiffer Beach Arch
Pfeiffer Beach, it is easy to miss the turn. Look for the turnback to Sycamore Canyon. If you get to the Post Office, you went to far.
Garrapata is also popular, as it is the first beach in Big Sur when coming from the north.
But be careful on the beaches! Sneaker waves can happen!
We got lucky. We went to Garrapata once and the water was quite far out. The kids went out on some rocks while we milled around on the beach. Few minutes later, a sneaker wave washed in. I told the kids to hang on the rocks as we backpeddled up the beach. The water completely surrounded the rock, but they hung on and were good. My wife though, she was pregnant and her center of mass was not where she thought it was. She fell, the wave washed over her, and the day was ruined.
Point being, when you go down to the beach, spend a few minutes watching the surf before going down to the water.
Go hike!
Last fall while we were down there, one of my sons and i did Whale Peak.
https://www.alltrails.com/trail/us/california/soberanes-point-and-whale-peak


I've also done Doud Peak. It's tough. Don't know the current status of the trail, Rocky Ridge was open when I did it 10 years ago.
https://www.alltrails.com/trail/us/california/doud-peak

Enjoy!