^ I said less than an hour because it doesn't seem like a whole lot of time passed from the time Enterprise left Earth to reaching Vulcan. Remember the events of the film.
The Enterprise is delayed from departing with the other ships for several seconds because of Sulu.
Pike orders maximum warp to Vulcan.
McCoy sedates Kirk.
Pike orders Checov to give mission broadcast. Which usually is given after the ship has began it's course. Not several hours later. Checov says they'll arrive in Vulcan in 3 minutes upon completing the mission directives and information about the lightning storm in space.
Returning to the medical bay we see McCoy with a change of cloths and discovers Kirk awake with swollen hands. It seems McCoy left Kirk on the bed, changed and came back. If he had been carefully monitoring Kirk for hours. Kirk's swollen hands wouldn't have caught him by surprise.
Kirk spends the next 3 minutes running around the ship looking for Uhura before going to worn Pike on the bridge.
The ENT was only delayed seconds by Sulu's blundering with the external inertial dampener. The ENT should've arrived while the fight with the Narada was still taking place.
We can just hand wave the discrepancies away and say that the film is moving at the speed of plot.