Vana Tom is the biggest and most well-known hostel in Tallinn. If you arrive in the off-season and are looking for company, you'd do well to book here as the majority of travlers end up here. The location is in the old city near the Town Hall and withing walking distance of most of the sites of Tallinn. There are several popular discos and night spots on the same street.
Accommodations are quite nice and far above the typical Eastern European hostel. Dorm rooms (six to eight bunks) and private rooms are available. The dorms are segregated by gender. The hot water is readily on tap and there is a kitchen for those who self-cater. The only downside is that Vana Tom (used to be the Barn) is a bit highly-priced for a youth hostel. However, it is far cheaper than any B&B or low-end hotel in the old city and does offer discounts for HI members and Peace Corps.
If you're looking for a cheap, clean place to stay and proximity to sites and nightlife is your main goal, this is where to stay. The average guest here is in their 20s, so it may not be appropriate for those who want to bed-down early. Also, the street noise can be a bit much as the hostel is below a popular strip club! Directly next door is a very nice Chinese restaurant that I can highly recommend.