General:
* Cover
* Throw
* Spread
* Rug (especially if it's a thick, woven blanket)
* Comforter (for a heavier blanket)
* Quilt (for a layered blanket)
* Afgan (for a knitted blanket)
* Sheet (for a thinner, lighter blanket)
Figurative:
* Veil (to cover something)
* Shroud (to cover something completely)
* Mantle (to cover something with a cloak)
* Layer (to cover something in multiple layers)
The best synonym depends on the specific meaning and context of the word "blanket" in your sentence.