I've got a couple of old chairs for my office that have 1 3/4" strapping on the seat that need replacing. Looking around, it looks like jute is the best option (I've tried marine fiberglass strap, which was the best option available within walking distance, and that was a disaster!).
Where do you get it, though? Should I be looking in hardware stores or fabric stores?
Check in Upholstery Fabric or Arts and Crafts stores if you want to source it locally. But, be forwarned that Jute upholstery webbing, also sold as burlap webbing, is a specialty item. You will probably end up having to mail order it. If I can't order it directly from the weaving house, I tend to default to Amazon.
I don't work much with straps and webbing, but use a lot of 1/4"-1/2" diameter rope for outdoor knotting and rigging projects. I usually end up making the heavier ropes out of twine via
But using a power drill and an eyebolt with an opening cut into it instead of a rope spinner.