How far did Watney drive to get to the Pathfinder in "The Martian"?

Exactly distance unknown, but likely somewhere between 464.634 miles and 600 miles.

It's not directly spelled out in the film. However, in Chapter 8 of the novel, the following discussion takes place:

“Watney’s on the move again.”

...

“Still going in a straight line,” Mindy said, pointing to her monitor.

“I see,” Venkat said. “He’s sure as hell not going to Ares 4. Unless he’s going around some natural obstacle.”

“There’s nothing for him to go around,” Mindy said. “It’s Acidalia Planitia.”

“Are those the solar cells?” Venkat asked, pointing to the screen.

“Yeah,” Mindy said. “He did the usual two-hour drive, EVA, two-hour drive. He’s one hundred and fifty-six kilometers from the Hab now.”

...

Pathfinder!” Mindy said. “He’s going to Pathfinder!”

“Yup!” Venkat said. “Now we’re getting somewhere. It’s like eight hundred kilometers from him. He can get there and back with supplies on hand.”

So, we can see from the novel the types of distances being talked about here - but it's not clearly spelled out what the exact distance between the two locations is and we know Watney's path is slightly complicated by the routes he has to taken in the rover.

But if we assume his 156km are in the direction of Pathfinder (a logical assumption) and we assume Venkat is correct with his 800km assertion, it's about ~950km, which is ~590 miles.

However, as the Watney's Hub is described as being in the Acidalia Planitia and Pathfinder is known to be in Ares Vallis, the exact distance as the crow flies between the two can be calculated.

And someone has already cleverly done this using Wolfram. The answer is 464.634 miles:

Therefore, this is the minimum travel distance Watney had. So the exact distance he had to drive is unknown, but it's somewhere between 464.634 and ~600 miles.

The HAB and Watney's science'd out makeshift base is located in the Acidalia Planitia. We are given its exact Lat/Long Coordinates in the book:

The Hab's at 31.2 degrees north, 28.5 degrees west. What do you see?

The Carl Sagan Memorial Station, formerly known as the Pathfinder Lander is in the Ares Vallis. It's exact position is:

19° 7' 48" North - 33° 13' 12" West

The distance between the two as the Martian Raven flies would be 475 miles. As Watney has to circumnavigate martian hills and rocks, his actual mileage would have been slightly larger. He gets lost for a while, and has to roam the desert in a general North direction. Round trip, that's almost 1000 miles. It took around ten Sols each way to recover the Pathfinder. He found it on Sol 82:

Sol 82 - Victory I found it

And returned by Sol 93~94.

I found the Hab signal today. No more chance to get lost. According to the computer, I’m 24,718 meters away.

This is almost half of the distance that Watney had to travel to reach the Ares 4 MAV. That was 2000 miles, one way.

A very neat map can be found at Andy Weir's "The Martian" Map which includes a Google Map with pinpoints for Watney's travels for various days, and coordinates based on book quotes.

This is actually one of the underrated parts of the movie. The distance is almost half of the one he makes to the Ares 4, if not more, and yet no apparent preparation like the atmosphere "bubble" on the top of his rover is needed, and heating (he did have the nuclear device tho). But still, for the trip to Ares 4 he does shit load of preparation, but he just like casually drives half the distance (which is 1300-2000 miles based the answers provided here) like it's nothing. It should have been given more significance in the movie, don't know about the book because I haven't read it yet.