Staying at the Light House was a pleasure. Gavin and the rest of the staff are very nice people, and you can borrow towels, adapters, and whatever for just a small deposit you get back. You get your own locker for free in your room. The place was clean, and the beds were comfy. Best of all, it felt like you were a guest in someone's home. It's also walking distance to Waverley Station and Prince's street, where you can grab a nice bus tour.
Staying at the Walrus was my best hostel experience yet and one of the highlights of my trip. The staff was awesome — very helpful, cool people likely to grab a pint with you at the hostel bar when their shift is over. The location is great — walking distance to Big Ben, Buckingham Palace, and South Bank. If you wish to go elsewhere, it's literally 300 meters from the tube station. The atmosphere was the best. Met lots of really cool people in the bar, one of whom I went sightseeing with!
If you're American, St. Christopher's will probably remind you of a cross between an Urban Outfitters and Buffalo Wild Wings where the YOLO crowd intersect with hipsters. It's a very clean place with wonderful "pod" beds that give you privacy and a nice place to charge your phone and a locker under it. The location isn't great — you absolutely have to take the metro to get anywhere, and the staff is a little snotty. However, it's cheap and clean. BYO-bedding and padlock to avoid rental fees.