At the top of the marble staircase from the ground floor is the first floor. The Entrance Hall and Great Hall are several stories tall, so they extend into this floor from below.
We never actually visit a Muggle Studies class in the books, but we can determine almost for certain that the classroom is on the first floor because, in order to get to her Muggle Studies exam, Hermione stopped at the first floor while Ron and Harry went on (PA16).
Harry and the other Gryffindors have a new Defence Against the Dark Arts teacher every year, but the classroom remains the same. In the films, a huge dragon skeleton hangs over the classroom until it is dropped and smashed by the pixies which Lockhart brought into the first Second-Year class of the 1992-1993. This is only a film invention, however; there is no mention of a dragon skeleton in the books, and if there was is probably wouldn't be in the DADA classroom. Dragons aren't Dark Creatures.
The room has windows looking out onto the grounds (out of which the pixies threw Lockhart's wand). An iron chandelier hangs from the ceiling (CS6), although it broke loose and fell during the pixie incident.
The DADA teacher's office and quarters are located on the second floor, which is represented nicely in the films with the use of a staircase coming into the classroom (see picture).
How do we know that the DADA classroom is on the first floor?
"(Lockhart) set off back to the castle with Harry, who was wishing he knew a good Vanishing Spell, still clasped to his side. 'A word to the wise, Harry,' said Lockhart paternally as they entered the building through a side door [from the courtyard, so they're on the ground floor]...Deaf to Harry's stammers, Lockhart swept him down a corridor [the ground floor corridor that runs opposite the Great Hall, probably] lined with staring students and up a staircase [so now they're on the first floor]...They had reached Lockhart's classroom and he let Harry go at last." (CS) (emphasis and comments added)
The History of Magic classroom has a blackboard through which Binns enters and exits the room. It also has a window through which Hedwig could enter; the window has thick glass and a narrow ledge (OP17). Just up the corridor from Binns' classroom, in the direction of the marble staircase, is a window with a view of Hagrid's cabin (OP17).
How do we know that the History of Magic classroom is on the first floor?
As they were shunted along in the throng, Colin Creevey went past.
But Colin was so small he couldn't fight against the tide of people bearing him toward the Great Hall; they heard him squeak, "See you, Harry!" and he was gone.
The crowd thinned and they were able to climb the next staircase without difficulty...
...they turned a corner and found themselves at the end of the very corridor where the attack had happened. (CS9).
McGongall's office is decorated with a lot of tartan plaid. She keeps a tin of biscuits on her desk and usually, the Quidditch Cup on her shelf. Her office has a fireplace with a mantelpiece, and the entrance is evidently within easy walking distance of Myrtle's bathroom (CS18). The fireplace can be connected to the Floo Network when necessary (HBP18). At least one of her windows overlooks the Quidditch pitch (PA9).
Some of the corridors along the route from her office to the entrance to Gryffindor Tower have windows overlooking Hagrid's cabin (HBP18). To get from the DADA classroom to McGonagall's office, take a corridor from the DADA classroom to the nearest flight of stairs leading down; McGonagall's door is on the left (OP12)
How do we know that McGonagall's office is on the first floor?
This one's easy. In PS15 it says "Filch took them down to Professor McGonagall's study on the first floor..."
Hospital Wing 1992-1993 
lots and lots of beds with white sheets
Madam Pomfrey's office
bedpans (Ron once had to scrub them for detention) (PA9)
moved to the third floor in 1995-1996
How do we know that the hospital wing is on the first floor in 1992-993?
Harry leaves the hospital wing, intending to go up to the seventh floor and the Gryffindor common room. He gets to the floor above the hospital wing and he is at Moaning Myrtle's bathroom. Later in that chapter it states that they go up the marble staircase to get to the hospital wing (CS13).
Possible plan of the first floor
This map takes the details from the books into account as well as the standard structure and architecture of castles. While not canon, this map is probably as close to the "real thing" as we're ever going to get. NOTE: This map was drawn in 2006, so a few details might not be correct if they came from book seven or interviews Rowling gave after that time.