as far as I know, there is no such aircraft. Simply because it would be very hard to realize. The cockpit is at the very front of the aircraft. Followed by the cabin.
Even large modern cockpits are comparably small and don't offer a lot of space. All modern passenger aircraft are designed in such a way that the front door or doors (if one on each side) are located right BEHIND the cockpit. These doors are also used for the flight crew, to get aboard the plane, passing then through the cockpit door.
Meaning not to have a cockpit door, would mean that the cockpit would have to had its own door, which could only be used by the flight crew to get inside and outside. This would mean a way larger cockpit and would probably not make a lot of sense, given that most aircraft are already pretty scarce when it comes to free space.
The cockpit door of all modern aircraft however, is locked from unauthorized access. We have a switch in the cockpit, where we can put the door into auto, unlocked or locked mode. If unlocked, the door is open. If locked, the door is closed and cannot be opened by anyone. In standard, auto-mode, doors are locked but can be opened by cabin crew, usually by entering a key combination. Also the side cockpit windows can be removed in case of emergency and serve an an emergency exit for the pilots, which is used only by them. To leave the aircraft this way, a rope is needed. One of these ropes is part of the emergency equipment of both, the PIC and the PNF/FO and is found in a storage located on the upper side to of the cockpit to the left and right.
Smaller aircraft and general aviation planes usually don't employ a separate cockpit. Cabin and cockpit are just one big space.