The best replacement for bins is baskets.

The best alternatives to bins are rated as following:
★★★★★  baskets
★★★★  containers
★★★  drawers
★★★  totes
★★  tumblers
★★  7stacks
★★  silos
★  sanji
★  trays
  compost tumblers

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

Other search terms related to bins and their ratings are:
★★★★★ shelves
You have in mind a companion for bins and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of bins in all years. Click on graph for more.
bins
baskets
containers