Oh, how I love Kex Hostel. Where do I begin? The main floor is a lounge that is also a coffee shop, library, bar, and restaurant. There's an outdoor patio that's the ultimate hangout, with wagon couches and twinkle lights. The decor is hipster to a T. They play great tunes 24/7: chill music during the day, and a DJ spins at night. It's a great place to start your night out in Reykjavik; come 6 pm, it becomes very lively with other travelers. The wifi is free and fantastic. The food is fresh, delicious, and affordable. I still crave their strong, hot coffee. There are lockers in each room to store your stuff safely. The hostel is so close to one of Reykjavik's main drags, Laugavegur. It's also on the water, which means great views of the bay.
Have I convinced you yet?