Assuming a helium balloon, it moves back toward the rear.
When you accelerate, the gas in your car behaves like a fluid, piling up in the rear of the vehicle. Helium balloons climb up the density gradient of air, essentially seeking the lowest density point.
That area of low density is at the front of the car as you accelerate. So, the balloon moves forward as you accelerate.
What matters is that the direction of the buoyant force is precisely opposite the direction of the overall force acting on the fluid (because that's what keeps the hypothetical fluid that your balloon displaces from moving due to said overall force). Importantly, this overall force needs to be measured in the reference frame of the fluid, which in this case is accelerating.
OK, so let's draw out a force diagram on the air inside the car. There's a force upward from the floor, exactly balanced by the force of gravity down. There's similarly a force from the back of the car , which is what's accelerating the air, from the point of view of a non-accelerating observer. From the point of view of an observer in the car, however, the air is _not_ accelerating, but the force from the back of the car is still there. So there must be a force backwards on the air, to balance the force of the back of the car. You can call it "inertial force" or "gravity" (in the general-relativistic sense) but the upshot is the same: the overall force on the air is down and backwards, so the buoyant force is up and forward, along the same line. For a helium balloon the buoyant force is stronger than "gravity", so it goes up and forward.
Not my proudest moment.