Living in the Netherlands, you might not want to stay in your city as there is a lot to explore in the Netherlands. Make sure you'll purchase a public transport card. It allows you to travel with all public transport within the Netherlands. Also regularly check Hema, Albert Heijn and even Kruidvat as they sometimes offer day tickets for the Dutch railway company at a discount rate.
However, not only the Netherlands has a lot to offer. City tripping in Europe is quite easy, and there are multiple options to get cheap travel deals. The Dutch Railway regularly offers pretty good deals for city trips all over Europe. However, you don't have to travel far. Hollands neighbouring country Germany is more than eight times the size of the Netherlands and easily accessible per train. Like NS Internationaal the German railway company Deutsche Bahn offers pretty cheap saver fares worth checking not only for travelling within Germany but within the whole of Europe. Another great opportunity to travel within Europe is an interrail pass. With the Global Pass starting from €200 up to €500 you can travel a certain amount of days in a month within the whole of Europe. Also, Holland's smaller neighbour Belgium has a lot to offer. Within two and a half hours you drive from Amsterdam to Antwerpen, and within three hours you're in Brussels, Gent or the picturesque Bruges. Check booking.com for a nice accommodation.
If you are planning on travelling by plane, use Skyscanner or Google Flights to find the cheapest rates.