Dumping into different spots to spread it out could be a solution. It would add expense to the process, though, and we know how capitalism handles that. As for aquifer charging, the brine is thicker than what was taken out. This adds to the problem in that you’ll need much higher pressure to drive it, or you’ll clog the system at the output point.

If you’re going to go the route of least expensive solution, find an area that is unattractive to human life, preferably a desert near the ocean. Pipe in the seawater, using RO to remove as much fresh water as possible. Then take the brine and send it out to evaporation beds covering a large area. You can recover some more water through that process, but, most importantly, removing the water and leaving the salts and minerals requires little energy input this way. The downside is the acreage required.

If you had a geothermal vent to provide heat, it would make the entire process almost carbon-neutral.