(covers information from several alternate timelines)
A cockpit was the forward section of an aircraft or spacecraft where the pilot and any additional crew were seated.
The F-104 Starfighter had a one-seat cockpit with the avionics positioned in front of the pilot. (TOS: "Tomorrow is Yesterday")
Earth's first warp ship, the Phoenix, had a small four-meter cockpit made from titanium, with enough room to seat three people. (Star Trek: First Contact)
United Earth Starfleet shuttlepods had a seat for one pilot in the forward section, and room for up to six passengers in the rear. (ENT: "Broken Bow", "Fight or Flight", "Terra Nova", "Breaking the Ice", "Fortunate Son", et al)
The NX-Alpha and NX-Beta craft had small cockpits, with room for two people. (ENT: "First Flight")
The cockpit of the Delta Flyer included a reduced seating area for the pilot with flight controls designed, for aesthetic reasons, to resemble those of 20th century aircraft. (VOY: "Extreme Risk")