Purification of Laboratory Chemicals (a generally accepted reference book for methods of purification of common chemicals) appears to agree with your procedure:
N-Iodosuccinimide [516-12-1] M 225.0, m 200-201 °C. Crystallise it from dioxane/CCl4. It iodinates arenes in triflic acid. [Olah et. al. J. Org. Chem. 1993, 58, 3194, Beilstein 21/9 V 544.]
As you point out, carbon tetrachloride is difficult if not impossible to get hold of now, so the methodology will not work.
The most obvious thing to try would be the method for the purification of NBS, however NIS is not tolerant to recrystallisation from water and from previous attempts doesn't achieve anything.
Depending on what you're doing with the NIS, I've often had success in simply dissolving in solvent and washing with sodium thiosulfate to remove any liberated iodine. Drying and evaporation then gives cleaner, though probably not pure NIS.
Also note that NIS should be stored in the dark at reduced temperatures to prevent decomposition (which is noted by the appearance of an orange/brown decoloration).