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Hi Julie!  I am a huge fan of the Hague.  Here are a few suggestions:

The Binnenhof (parliament buildings).  It's free, beautiful, and centrally located.  Plus the little pond (canal??) lined with flags is a nice sight too.

Noordeinde Palace and the Peace Palace are two more lovely tourist attractions.  Noordeinde Palace is right on the Hague's most expensive shopping street, so it's ideal for a bit of window shopping too.

If it's a nice day and in you're in the mood for a bit of whimsy, the Madurodam (miniature village) is a fun way to spend a few hours - though it does cost. 
Also to do on a nice day: take tram 17 down to Scheveningen beach.  It's a lovely walk with lots of food vendors (try the kibbeling at Simonis!) and beach clubs, and a pretty fun if rather touristy nightlife too.  They have an aquarium there but it is rather expensive and small.  Alternatively, they have a fun arcade.  You can also walk down the peer and climb up the bungee jumping platform to get spectacular views.

If you like museums, the Escher museum is awesome!  It's a collection of Escher's optical illusions, housed in a beautiful old house.  The Mauritshuis is also a good one - it's a small museum with a nice collection and a few ver Meers, including the Girl with the Pearl Earring.

Het Plein, of course!  For food, drinks, dancing, and an overall excellent atmosphere, it really can't be beat.  It's always full and buzzing after work for the borrel - I love people watching there, perhaps with some deep-fried kaas stengels in hand ...  The Miller's has amazing (albeit slightly pricy) food and the Cloos plays great popular music if you're up for a fun night.
There are also a lot of great restaurants off the shopping streets, sort of across from the Buitenhof. 

For a lovely little walk, you could wander along the Lange Houtstraat.  There isn't necessarily anything to do there but it's a beautiful, tree-lined street where a lot of important companies have offices in old monumental homes.

For cheap food try China Town - it's right by Het Spui and it's got so many fun places to try, Chinese and not so much.  Fat Kee for example has a secret dim sum menu that you have to ask for (it's not on their table menus), where everything is delicious and invariably priced at 4 euros.  Across from Fat Kee there's also a great Turkish bakery, but really all of China Town is a favourite of mine and you can find so much there! 

If you're outdoorsy check out Het Haagse Bos.  Behind Centraal Station, it's a more woodsy area with deer and birds and even wild bunnies!  It's quite large for a Dutch forest, with lots of different paths to take.

Finally, depending on how much time you have, you should definitely check out Leiden.  It's only a 10 minute train right away from Centraal and it'll cost you 3,60 without a discount card.  It's so close and yet so different from Den Haag - full of teeny little cobblestone alleys, lovely canals and medieval churches.  Go on Wednesday or Saturday for the market, and do the sample tour ...  hehe.  A delightful way to spend lunch!