Home to the well-known Uppsala University and about 200,000 Swedes, Uppsala is the 4th largest city in Sweden. The city is almost a thousand years old and an important center of culture and commerce. There are plenty of young people in the city because of the university, and the vibe is pleasant and relaxed.
The hostels in Uppsala are of good quality and the prices are reasonable. If you book a dorm bed, you should expect to pay about 20 euros or a bit more, and around 30-40 euros for a double / twin per person. Uppsala hostel owners and staff are a great source of information when you're planning your daily activities, and there might also be bike hire available.
Most people get to Uppsala by train, utilizing Sweden's national train service (SJ). You can also get there by bus, which might be a bit cheaper. There is no airport near the city, the nearest being Stockholm's airport: Arlanda. As mentioned before, bicycle is the best way to get around from your Uppsala hostel. There is also public transport available, the bus is probably the best option.
Besides Uppsala University, the city has a very impressive Cathedral (called "Domkyrkan") that is well worth seeing. There is also a castle in the city, and several museums & gardens to spend your time in. If you're going to visit an Uppsala hostel during the summer, it's highly recommended to check if the annual Reggae Festival is at the same time (if you're into reggae music, that is). With many international performers every year, the festival is a very nice way to spend at least a part of your stay in Uppsala.