To enter the Abyss without doing the key quest you can simply go to either of the Fel entrances to the new champ spawns and run out of the spawn into the Abyss. You will not be able to run to Ter Mer (through the tomb of kings) but you will be able to bypass the Underworld and access the entire Abyss.
The entrances are in Hythloth (in the balron room with the stairs to the bottom level there is a cave entrance) and Deceit (on the bottom level in the main lich room there is a hole in the floor). Remember it is in FEL until you exit the spawn and enter the Abyss.
The entrances are in Hythloth (in the balron room with the stairs to the bottom level there is a cave entrance) and Deceit (on the bottom level in the main lich room there is a hole in the floor). Remember it is in FEL until you exit the spawn and enter the Abyss.