The Hague is the perfect alternative for the frantic Amsterdam. If Amsterdam is crowded, cheerful, strident, the Hague is mellow, harmonious and much more sober. You will not find here the typical young crowd looking for drugs and "fun" (at least not much). Tourism in the Hague is oriented towards culture and relaxation. I have visited the city twice and it is one of my favorites. In my opinion, the best time to visit The Hague is summer when you can visit the Scheveningen beach and enjoy good weather.
The Hague is the "political capital" of the Netherlands. Therefore one of the main attractions is the Binnenhof (picture above) which are several buildings that correspond to the Executive and Legislative branches of the Dutch Government. It is possible to visit the Binnehof inside (at least the Ridderzaal, the main building of the complex) but I have never done the tour because they only offer it in Dutch (surprisingly). Recently I checked their website and apparently they provide audioguides for the tourist (but you are still obliged to be within the tour in Dutch).
If Amsterdam has the Rijksmuseum; The Hague has several museums that will be the envy of any major city. The two times I have been in the Hague, the Mauritshuis Museum was closed for renovation. Hence, I can only review the Gemeentemuseum which exhibited part of the Mauritshuis' collection. There are three major works of arts that you must see while you are in the Hague: Johannes Vermeer's Girl with a Pearl Earring; Rembrandt's Anatomy Lessons and Victory Boogie-Woogie the last work (unfinished) by Piet Mondrian. The Gemeentemuseum also has a vast collection of De Stijl in addition to Mondrian and many objects from Batavia (Jakarta). There are other museums that I did not visit. I specially regret not visiting the Escher Museum (next time, I promise!).
I strongly recommend to visit the "Peace Palace" (the current headquarters of the International Court of Justice and the International Court of Arbitration). The building is very beautiful inside and it is decorated with gifts that come from many nations. You can only visit the building within a
guided tour and photography is not allowed inside. You will learn about how these courts mediate between parts involved in international conflicts.
For those who love nature, there are two huge parks inside the city. You could go to the Haagse Bos or you could cross the Schevingse Bosje walking a long the channel and reach to the beach. There is a bonus inside this path, the Madurodam, a museum of minuture buildings. A good trip to the Hague includes both culture and nature.
Regarding the food, well, The Hague is in The Netherlands which pretty much sum it up the available choices. You could spend a fortune to eat decently or you can take a risk. My best meal was in a chinese/indonesian/korean restaurant close to the
Haagse Markt (one of the largest outdoor market in Europe). There is a large diversity of food from Asia. A safe option in The Hague is chicken Satay. Of course, there is always an Albert Heijn (Supermarket chain) near that could save the day.
A trip to The Hague could be combined with a trip to Delft (where you could buy this beautiful blue-white pottery) or even Rotterdam. If you wan to experience the Netherlands in a different way, The Hague is certainly a great choice.