Where is Voyager 1 (or 2) going? In which direction?
Stars and gases at a wide range of distances from the Galactic center orbit at approximately 220 kilometers per second.


From Wikipedia

That's much faster than the Voyager probes relative to the Sun (Voyager 1: 17 km/s). Hence the probes will orbit the galactic center roughly the same way as our Solar System, even after occasional hyperbolic encounters with other stars.

Voyager 1 is travalling in the direction of Ophiuchus, seen from Earth. She's at or beyond the border of the heliosphere.