You don't mention it, but the most likely cause of moisture in your fireplace is lack of a chimney flue cap.
If you have a cap, the second most common cause of moisture in your firebox is the mortar cap that goes around the terracata (or other composition) flue and out to the chimney bricks, sealing the area from outside moisture, has cracked or broken, allowing moisture to get down between the flue and outer chimney brick. If its just cracks, you can seal them with roofing tar (from a caulking gun). If it is beyond repair (cracked, broken, etc) you may have to go up on the roof, break out the old mortar cap, mix up a batch of new mortar and reinforcing screen and replace it. Not too difficult a job.
A good chimney sweep can look down the flue and tell you if its in good repair or not. I would need a lot of convincing to install a stainless steel or concrete liner.
If your exterior chimney bricks do not have stress fractures/cracks, is not listing or settling unevenly, then you probably do not need to replace it. If indeed moisture was running down the inside of the chimney brick (through a leaky mortar cap), soaking the brick mortar, then freezing and thawing, this would help explain the spalling. If the brick mortar is cracked through and through, you may have to remove courses of bricks and remortar them. If the mortar joints look ok in general, you may be able to chisel out the cracked mortar and repoint. One other possibility is that the original mortar was made with too much water and allowed to dry too quickly, which would make the mortar weak and brittle. I have yet to see a chimney mortar job so bad the chimney had to be taken down and rebuilt, but I'm sure its possible. Some poking around the mortar joints should tell you this.