Where is the most effective spot to item farm?

The best bosses to farm for items are BNK3R, Warrior and Terramorphous. You can't fast travel to these locations, so what you need to do is kill the boss, quit out of the game and then restart the game. The boss will be back and you'll be right at their front door instead of having to run the respective gauntlet before each boss.

Note that Orange/legendary drops are extremely rare except from certain bosses (even then orange drops are absurdly rare. Killed BNK3R 20 times this weekend and got squat). Farming is an effective way to get purple/blue weapons from any boss, but you'll need to target your farming if you want the legendaries.

Also note that Terra always spawns at level 52, so if you aren't level 50, don't bother. See also my guide on killing the crap out of Terramorphous. Similar to the advice in that question, The Bee is an effective way to farm any boss; it used to be insanely easy, now it's just significantly helpful. The Bee has been nerfed (more specifically Amp Shields in general) so the boost is less significant for multi-projectile weapons, so if you're using the Bee, try a single bullet per shot, high rate of fire weapon like a Spinigun instead of a shotgun.

BNK3R in particular is easy to farm for Assassins since the Bore skill is bugged for him and sometimes he'll take repeated hits from it (with increasing damage) and die in very few hits (or one).

However, regarding farming before playthrough 2...Don't farm before playthrough 2. Actually you need to be in playthrough 2.5 (e.g. complete playthrough 2) to get the best items possible. Don't farm until your level is maxed out; unlike Borderlands 1, damage follows an exponential scale in Borderlands 2. This means almost immediately after playthrough 1, orange level 30 guns are total crap compared to green level 35 guns. Ditto even up to level 45 guns. Everything is crap until you hit the level cap, just play normally until then and don't worry about farming.

In the wildlife exploitation center, if you haven't received the mission from Tannis, is the mission "Doctor's Orders". DO NOT collect any of the echo recordings. Instead fight your way to where the 2nd echo is (just after the super badass loader ambush) and in the room where the recording is there are 4 boxes. Opening each box without grabbing any echo recordings will almost always yield 4 loot midgets/loaders. Killing these at higher levels can yield aprrox. one legendary gun per 4 loot midgets/loaders. I myself after 4 runs on this location have received the corporate bitch, the impetuous hellfire, the vengeful ker blaster, and the 2 for 1 gunnerang. In my opinion it is the most effective farming method.