The best replacement for wool is cotton.

The best alternatives to wool are rated as following:
★★★★★  cotton
★★★★★  nylon carpet
★★★★  fleece
★★★  polyester
★★★  down
★★★  cotton socks
★★★  cashmere
★★  acrylic
★★  cotton suit
★★  polyester suit
★  down comforter
★  cotton dress pants
★  synthetic rugs
★  synthetic carpet
★  hair
★  woolen
★  cotton rugs
  polypropylene
  synthetic area rugs
  fiberglass insulation
  polyester rugs
  cotton blazer
  synthetic rug
  polyester suits
  wool blend
  sandpaper
  cotton sweater
  olefin
  cotton rug
  polyester warmer
  nylon rugs
  cotton pants
  polypropylene rugs
  silk duvets
  wool
  cotton and rayon
  polypropylene carpets
  worsted wool suit
  wool felt
  polypropylene rug
  worsted wool
  cashmere warmer
  man made carpets
  mohair
  synthetic carpets
  linen
  yarn
  down coats
  nylon carpets
  wool blend braided rugs
  polypropylene carpet
  down duvet

Your alternative for wool is not listed? Suggest!
Speaking about wool, one probably shouldn't forget about lycra.

Other search terms related to wool and their ratings are:
★★★★★ lycra
★★★★★ pom poms
★★★★ felting
★★★ sheep
★★★ linen
★★ cashmere
★★ cotton
★★ mohair
★ natural dyes
★ killing sheep
You have in mind a companion for wool and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of wool in all years. Click on graph for more.
wool
cotton
nylon carpet