When you bet the flop, your probably gonna get a reraise if he has a hand that will pay off your straight aside from a monster. Since you dont want a reraise here but you do want him to pay you off I would check the flop.

The call on the turn was probably a bad move unless you knew he would pay you off huge if you hit. Without any read I would say you can expect to get paid out about $15-$30 on the rive if you hit so I dont think implied odds would be that great, however if you knew you could get him to call or reraise your $60 bet then its a good move.