To get to the DLC zone, you need to use fast-travel to Badass Crater of Badassitude. If there are two zones in the brackets, this means that quest starts in the first one and ends in the second one.
Story related quest list:
- Highway to Hell (Badass Crater of Badassitude)
- Welcome To The Jungle (Badass Crater of Badassitude/Torgue Arena)
- Battle: Appetite for Destruction (Torgue Arena)
- Burn, Baby Burn (Torgue Arena/Pyro's Pete Bar)
- Battle: Bar Room Blitz (Pyro's Pete Bar)
- ChopSuey (Pyro's Pete Bar)
- A Montage (Pyro's Pete Bar/Badass Crater of Badassitude)
- Eat Cookies and Crap Thunder (Badass Crater of Badassitude/Torgue Arena)
- Battle: The Death Race (Badass Crater of Badassitude)
- Get Your Motor Running (Badass Crater of Badassitude/Southern Raceway)
- Breaking and Entering (Badass Crater Bar/Forge)
- Knockin' on Heaven's Door (Forge)
- Battle: Twelve O'Clock High (Forge)
- Kickstart My Heart (Forge/Badass Crater Bar)
- Long Way To The Top (Badass Crater Bar/Torgue Arena)