Should you patch or replace a concrete sidewalk?
If your walk has a few hairline cracks but still sits level and drains, I'll tell you it can be patched or left alone, because tearing out sound concrete wastes your money. When sections have lifted over roots, sunk into low spots or tipped toward the house, a patch won't last, since the ground under it is still moving. Then the honest answer is to break it out, fix the base and the route, and pour new.
What shapes the cost of a concrete sidewalk
Size sets most of the price, then the ground work under it, such as breaking out an old walk, cutting back roots and packing the base. A plain broom finish costs less than decorative concrete like stamping or color, and pouring the walk on the same trip as other work, such as garage floor concrete, can save a separate setup. If the budget is tight, I'd trim the finish before the base, because a fancy top on loose dirt cracks just the same.