If you run flat pedals, rather than clipless, then the Adidas Berm is a top bet. These lightweight shoes are mountain bike-specific, with fairly stiff soles. The padded tongue and raised ankle offer both comfort and protection, though there's less pedal feel than with some flat-soled shoes.
It’s good to see a retention strap that keeps them in place and protects your laces at the same time. Unlike soft, flexible skate shoes, the Berm’s sole is stiff yet offers ample flexibility for pedal feel and walking. The soles grip the pedals well, too.
Laces are kept out of harm's way with a Velcro strap. This isn't to all tastes, as trimming the laces is easier and reduces bulk.
If you want flat pedal grip and protection, these are a good choice.