Straight to the dome was a relatively popular term during the 90s for being super high and spaced out on drugs, usually weed. It is also often used to say you're going to get super high. The term "Straight to the dome" is a variation of "Straight to my dome" meaning the drugs went straight to your head.
Stoner 1: Dude, wanna get high.
Stoner 2: Yeah man, let's go straight to the dome.
Stoner 1: Fuck dude, I punched so many buges, I'm so spaced.
Stoner 2: Dude we went straight to the dome.