Where can I farm for a legendary in vanilla Borderlands 2?

For easy loot, if you haven't already done it, I'd start by redeeming every single golden key I could and open a bazillion golden chests. Though, as mentioned in a comment, Golden chests only drop epic (purple) loot, not legendaries.

You can look here for a list of a ton of golden key codes (bottom of page) http://orcz.com/Borderlands_2:_Golden_Key (red codes are usually expired, black ones usually works, but not always, try sorting them by date and starting from the most recent)

Otherwise for farming, it depends on what you want, I'd suggest going through a list of legendaries (http://ca.ign.com/wikis/borderlands-2/Legendary_Weapons here for example, there are many online), finding one you like and farming it. Of course if you do not have any DLC, make sure the enemy that drops it is available in the vanilla game.

On my second playthrough, I got a grenade mod called "Lobbed Bonus Package" from Bewm Boom (the second boss). Apparently both Bewm and Boom can drop it, so it's one of the easier legendary weapons to farm.

It's awesome. It destroys everything in a 50 foot radius.

Here is a list of weaps and their location. Or you can go to Wildlife Preserve and farm loot midgets there.

Farm bosses like the Warrior (Conference Call shotgun), Boll (Fastball grenade) and Bewm Boom (Bonus Package grenade). I forgot if there's any more enemies that drop legendries, just look on the Borderlands Wiki.