Not every karting venue is a children's party destination. 3 tracks around Los Angeles work as an adults' evening out — late sessions, a bar or lounge on site, and racing that holds its own without the arcade.
Evening availability is the thing that varies most: some venues hand late slots to leagues or private bookings. Check session times on the venue's page before you plan the night around it.
K1 Speed Chula Vista, K1 Speed Santa Clara, Big Bear Speedway Go Karts — all listed below with ratings and contact details.
Some of the venues below have a bar or licensed lounge, which is part of why they suit an evening out — but drivers are not served before racing at any reputable track. Check the individual venue page for what's on site.
Go Karting USA lists 7 operating tracks around Los Angeles — see the full Los Angeles guide for all of them, not just date night karting venues.