A tidally locked planet does NOT experience day-night-circles: one side (around the "hot pole") is always pointing to the sun, the other (the "cold pole") points away. The system is rotation symmetric around the sun-planet axis, so there is no preferred direction orthogonal to the hot-cold direction. The starfield rotates around the planet once a year (and is not visible from half of it), so I doubt it would figure into cardinal directions.