St. Pauli may not be right in the city centre and we are not right beside a metro station. But if you like to see more than only other tourists running from sight to sight than you should think of a stay away from the main train station. Of course here are tourists too and you mainly meet them on weekends at the Reeperbahn.
Diving into the local life may be the tour of Alternative Hamburg Tours. http://www.alternativehamburg.com/tours.php "Oh yes, another sightseeing tour..." you probably think now. But this tour informs you about political situation, streetart and alternative lifestyle. A good base to start a chat with a local at our bar or anywhere else in our quarter.
If you still want to avoid guided tours and explore the area on your own, you will find soon more places recommendet by us.
For a start here are my recommendations:
If you need juicy meat between your teeth than i have 2 options. For burgerlovers it is "The Burger Lab" http://theburgerlab.de/ or you try "Erikas Eck" - german dishes likes Schnitzel or Rundstück warm. They are open from 5 p.m. till 2 p.m. next day http://www.erikas-eck.de/
Beerlovers find in our fridge a lot of new craft beer but if this is not enough you should try "Altes Mädchen" http://de.altes-maedchen.com/ (But: This place is not cheap - if you want to buy cheaper craftbeer you should visit the Craftbeer Store https://craftbeerstore.de) It is just nearby the Ratsherrn brewery and you can visit the brewery aswell.
For sophisticated Drinkers i recommend the Bernsteinbar http://www.bernsteinbar.de/ in our street. Good R'n B music and nice cocktails. At the weekend this is a crowded place and here you should not wear your most worn out stuff. ;)
Chill out: Prepare a nice picnic and take the harbour ferry 62 towards Finkenwerder. Hop off "Neumühlen" and chill at the riverside beach.
In summer i will start my "sundowner tour" again. Chilling at the deck of the ferry having a few drinks, watching the sun go down and chat. I am looking forward to this. (The harbour ferries are the only public transports where you are still allowed to drink alcohol in).
If you meet me in the hostel - just ask if you want to know more.