Gamla Stan = Stockholm's Old Town is the oldest neighbourhood of Stockholm. Here Stockholm was founded by Birger Jarl in medieval times and here the royal palace was built - which later burned down and a new palace was built instead. Gamla Stan is the heart of Stockholm and one should at least stroll around this area for an hour when visiting Stockholm.
It consists of many dark alleyways, cobble-stoned streets, red and yellow painted houses and three famous churches: the German church (Tyska Kyrkan), the Finnish church (Finska Kyrkan) and the Great church (Storrkyrkan). Of course nowadays there are a lot of souvenir shops in this area but also many small, unique shops that sell Swedish craft and fashion.
And you shouldn't miss out on the Ben&Jerry's ice-cream parlour if you are there and if you like Italian food, the Vapiano right next to the subway station is always worth a visit. But of course you can find many authentic Italian restaurants in Gamla Stan (they are just too expensive for my student budget ;))
So after you've visited the Royal Palace you can just stroll around the area, buy Swedish design furniture or just eat and relax in one of the many cafes and restaurants. (Lunch always is the cheapest option in Stockholm if you want to eat a warm meal!) Next to Gamla Stan you can find Riddarholmen - the knight's island. You just cross a bridge and you are in the most beautiful place of Stockholm. Sit at the water and enjoy the view on Stockholm's Stadshus!