Banglamphu - The district of Bangkok with the highest density of hostels. This is where I lived. I stayed at a recommendable hostel called Born Free Hostel owned by a Swiss guy. It's not too close to Khao San or Rattamburi which are a backpackers paradise at night, but a bit depressing during day time. Cause many stands only open at night. Just 5 min walk from Banglamphus Khao San night life area and you have a peaceful area to rest after exhausting sight seeing tours and long walks. It's also just 5 min from the river, close to the next Phara Express boat. You can just hop on the nearest pier and discover the city by boat.
Here are some impressions from Banglamphu. It's most entertaining during night of course.