I want to leave LA around 7pm and head towards Morro Beach. How is the highway at night?

Presumably, you mean Morro Bay. Hwy 101 is a major highway, divided and at least 2 lanes in each direction as far as San Luis Obispo, as is Hwy 1 in the section that continues on to Morro Bay. You can have a look on Google Maps Streetview.

Which route, or where's the starting point in L.A.?

I don't understand the question. It's multi-lane all the way, sometimes with a center barrier (sometimes not), sometimes divided/separated (sometimes not), etc. Depending on the day of the week and time of year, the first part (getting out of greater L.A.) will still be in heavy traffic to Santa Barbara. You'll likely reach the more scenic part of the drive after the sun goes down, so you'll miss that. A full moon might compensate a little.

Unless you are well rested and driving your own car, I would not want to go much farther than Santa Barbara after dark.
There is a Pacific Surfliner train that leaves Los Angeles Union station shortly after 7PM that goes to Santa Barbara.
There is an Amtrak bus that goes onward to San Luis Obispo.

Piece of cake. Little over 200 miles - three and a half hours?

The question is totally reasonable. People always recommend not driving Hwy 1 in the dark, but they are taling about Big Sur, not Hwy 101 south of Morro Bay.

Good point November.

Thank you so much. I did mean Morro Bay. I was worried about being tired and it being dark. Im going to do it

It's not the night you arrive from the east coast, is it? Your body clock will be at 10pm, not a good idea.

FWIW, most people don't find a three hour time difference to be that big a deal; a lot depends on whether you can sleep on the plane, how early you had to get up, and a host of other factors. 101 is easy driving.

Not sure what Tom Fuller means about not driving past Santa Barbara, still a divided highway all the way to San Luis Obispo where you will get off to go to Morro Bay. Easy drive. Seven is a good time to leave, you should miss most of the heavy traffic getting out of LA. Notice, I said miss most of the traffic, it will still be busy probably until you reach Ventura County.

Seven is a good time to leave unless you actually want to see the scenery past Santa Barbara.