Is this grammar correct for a tattoo with my fiancé: Ki’taxa vathia’ mes sta ma’tia sou ke I’da to me’llon mas?

Yes, it’s correct: “I looked deep into your eyes, and I saw our future.” I’d have used a more poetic verb for “see”, like atenisa “I stared right at” or antikrisa “I faced, I came face to face with”, but iða is fine.

Do use actual Greek script though. Κοίταξα βαθιά μες στα μάτια σου, και είδα το μέλλον μας.