Red P.
Yelp
I used to go to this place very often when I lived in St. Georg. A little hidden in a sidestreet next to the famous "Lange Reihe", this is the coffee shop to go on your walk around the district.
It is small, intimate, friendly and very cozy. The prices are okay. Not very cheap of course, but affordable compared to shops like Starbucks or Balzac (the latter is around the corner and by far the wrong choice). They offer a nice choice of small snacks, candy, soda, pastries and ... of course... coffee which comes in two sizes. Ever since I left Hamburg, I returned every once in a while only to find out that nothing has changed in Peaberries which definately is a good thing here.
They have rather restrictive opening hours and only very little place for seating. I suppose it is more of a "coffee to go" shop. Many people chose to sit on the benches outside by the Gurlittstr. which happens to be quite a nice promenade near the Alster.