The Problem: Suction-based bath toy baskets suck. Or rather, they don't suck. Hence, their suckiness.
The Attempts: A sampling of nearly every type of bath toy basket on the market, including one shaped like a giant frog (too heavy), a mesh basket like a laundry bag (too hard to get toys in and out of), and a basket on our bathroom floor (too much water where water was not supposed to be). I also invested in several 3M hooks designed especially for the bathroom on which to hang a variety of different baskets. Despite following the directions to a T and numerous retries, the hooks refused to stay. Nevertheless they did inspire my final solution!
The Solution: A clever combination of plant-hanging chains and a coated metal basket. The result is a relatively elegant bath toy basket that is easy to dump, easy to fill, and airy enough to let the toys dry.
The Cost: $19 for the basket at Target (I splurged for a more elegant look; I could have gone with plastic for much cheaper) and $5 for the plant hanging kits at Home Depot (which was actually cheaper, and prettier, than buying S-hooks and chains separately).
Alternatives/Modifications: Not everyone has a nice towel bar at the back of their bathtub; however, you could implement the same idea by looping longer chains around the end of shower curtain rods.