Round 1 Bowling & Amusement

Official Round1 website confirms karaoke rooms and extensive entertainment offerings including bowling, arcade, and private karaoke rooms

Official location page for Coronado Center with address and contact information

Reddit user comment: 'Round 1'

Comprehensive D&D Karaoke tournament venue: Round 1 Bowling & Amusement has private karaoke rooms and offers player slots ($5 reserve) with dice sets, event stickers, pre-filled sheets, karaoke mechanic powering up teams, more laid-back environment than typical bar scene.

If I remember correctly, I think Round1 in Coronado Mall has private karaoke rooms. I remember coming across that a year or two ago when I was looking at possibilities for some birthday fun for my step daughter.