Perhaps a Fuji XP120 Waterproof digital camera?
HERE for $150
Got one for DD and DW liked it so well she bought one for herself.
Has 5X optical zoom and 10X digital zoom.
Optical zoom is limited because of the lens being sealed (IE no external moving parts to get stuck with lint, dirt, sand).
Other no sealed pocket cameras will have more optical zoom because of the longer moving lens.
This IS the only camera that my DD has not destroyed (can't tell kids anything) so you will have to work really hard at ruining this one.