It's easy to find cheap, non-leather shoes; it's just a bit more difficult to find cheap, quality non-leather shoes. Athletic shoes are tougher than dress shoes. I go for a lot of long walks, so I want a shoe that first of all offers great foot support, and secondly will be durable enough to last 9-12 months (that's not bad: if you walk a lot, all shoes are going to wear away eventually, and if you find shoes for under $20, nine months is pretty good usage).
There's one thing I've found to look out for. If you are buying really cheap shoes, don't buy the ones that appear to have air pockets on the side of the heel. They're going to pop, fall out, or wear away very quickly. You just want a good, thick base of solid material.
The best brand I've found is Cross Trekkers, which you can get at Payless Shoes. Whenever I put on a new pair, I'm always amazed at how great my feet feel: the support is very thick, and a long walk is pleasant and smooth. Walking is easy when your foot is comfortably cushioned. I've found Cross Trekkers to be pretty durable, easily giving me the 9-12 months of usage I'm looking for.
It takes longer to find shoes without leather. Some brands clearly label the materials as including man-made materials, leather, or both, but some brands make it difficult, and some don't seem to bother labeling it at all. So cruelty-free shoe shopping is a little more challenging, but I actually usually end up with high quality shoes.