Taking the overnight ferry to Helsinki is one of the easiest (and most cost effective) trips you can make from Stockholm! You can book a cabin on one of the cruise ships that make daily crossings to the capital of Finland. The cruise consists of two nights on the boat and a day to visit Helsinki inbetween.
Helsinki is almost impossible to see in one day, but you can give it a good try before hopping back on the ship for your return back to Stockholm! (You would have approximately 6 hours in Helsinki before your ship departs again.) For cheap food, we recommend the Finnish version of McDonald's: Hessburger, but there are literally hundreds of other restaurants to choose from if you would like a more authentic Finnish meal! And if you have the time, catch the number 4 streetcar that will give you a nice trip around the central parts of the city in less than an hour!