I arrive at 11:30pm and have a flight out at 6:00am the following day. I plan to stay at the airport, but probably won't sleep until I hop on my next flight. What is there to do at the airport? Are there any airline clubs open the whole night? What time do the restaurants open/close?

The airline clubs are closed at night there AFAIK and the "restaurants" will be closed by the time you arrive. I'd recommend bidding on Pricline for a cheap room.

There will be nothing open - a seriously dead zone and likely they will make you exit security (travel to the main terminal and exit security). I agree that PL'ing something cheap in the area with shuttle service may be a much better idea.

I think previous posts are probably correct that it will be a hassle (or not possible) to stay in the terminal.

However, I do understand not wanting to get to a hotel at 12:30am just to lay down for a 4:00 am wake-up call.

I don't think this will work, but one long shot would be if you can get back into the B concourse, I seem to recall they have one of those 15 minute massage services right in the middle of the concourse with the chairs that you sit in and put your face down onto a sort of large circle of padding.

If you managed to get there, that would not be a bad way to take a nap as I am sure the employees are gone. Probably can't get there and police or cleaning crew would probably chase you away, but if you are wandering around late at night, worth a shot.

I won't feel the need to sleep until I get on the plane back. 6am EST = 3am PST. From what I gather, there isn't much to do inside the airport. I think I'll just find somewhere to sit and read a book.

Any suggestions on good locations to sit inside and/or outside security? Looking for a nice and comfy lounge chair. I haven't been to the airport, so the only knowledge I have about IAD is the terminal map on the website.

find a piece of floor in the main terminal, or maybe near the front window, there are no comfy lounge type areas at IAD ... unfortunately.

BTW - those massage chairs and area are covered, I do not recommend entering that area unless you want to deal with airport security in an unfriendly manner.

I very seriously doubt you will be allowed to stay inside security. I know from experience you can't at DCA so I am sure IAD will be the same.

http://www.sleepinginairports.net/usa/washington.htm

Check out the "Sleeping In Airports" website for info that may be helpful. Your best bet may be to pack an inflatable pool float or camping pad and an eye shade!

I know you said you didn't want to pay for a hotel but there is Marriott really close to the terminal itself. It isn't connected to the terminal but it is close by, in my defence I've not attempted to walk it.
http://marriott.com/property/propertypage/IADAP

My parents have stayed there on a Priceline stay for about $80.

You can walk to it but they offer a shuttle from the terminal which I would suggest; especially if this will be your first time at IAD.

I would also suggest the Marriott at the airport; they've got a bar and lounge. Not sure about the hours on those though. You can definitely walk to it, probably 15 minutes tops, unless you have a lot of luggage.

The walk from the main terminal to the Marriott is not all that easy. No sidewalks. One must either walk on the roads circling the parking lot, or cut across the parking lot, then across the same circling road, and then across private parking lots for office buildings separating the terminal from the Marriott. If I had not been there before, I would not strike out on foot after midnight on foot, unless young enough and no luggage. No threat of petty crime per se, just a dangerous kind of walking environment.

My suggestion would be to decide whether you want to book a room there and then use the shuttle bus, or if you really prefer to stay inside the terminal. There are some fairly comfortable rows of seats downstairs near the international arrivals and customs facility (far western end) where I might sit and even snooze for a while. Also smaller number of seats near the main exit point for domestic passengers on incoming flights, which is where you will probably exit into the baggage claim area from your incoming flight.

Also inclement or cold weather may be a mitigating factor when walking after midnight.

I have stayed at that property and it is a bit of a schlep from the airport.

I also remember being annoyed at how early stuff shuts down there.

All that being said it is the closest property to IAD and would be far more comfy than the floor or any chairs at IAD, it is just a horrible place to try to do this.

Best of luck.

At that hour, everything will be closed. If I wanted a comfortable seat for several hours to read a book, I'd Priceline a cheap rental car ($25-$35 hopefully?) and drive it somewhere nearby.