I would NOT do open toed sandals. Those are asking for injury IMHO.
We've done Stride Rite Angler fisherman sandles--DS wore those the summer he turned 2 and DD is wearing the same pair this summer at 2.5 (she has small feet). We've also done Keens.
My kids love their crocs but we let them wear them sparingly because they tend to fall down in them.
But they both do wear sneakers some in summer. DS has been wearing sneakers almost exclusively in summer for the last several years because his feet get too stinky in sandals, and he's super active so needs the toe protection.
My sweet boy 8/06
My beautiful girl 10/09