I've been looking for such a place too, no luck. We had a fave in the states and then in Hamburg. And yes, there is a difference.
Dallmayr and Tchibo are not that good, sorry.
In the meantime however, I found a place that sells very high quality italian vaccum packed beans -- it is a coffee shop that also sells and repairs espresso machines, on Schulstr. right near the RoteKreuzplatz station.
When I asked for advice, the owner actually asked me what brand machine I had and was familiar with the make and model of both our espresso machine and grinder (it's worth buying your own grinder), and made a very nice recommendation...the brand we use now is called Hausbrandt. I think he has enough turnover that the beans were fresh, but you could probably ask him about where to buy fresh roasted.
good luck, and please let me know if you find a place.
edit: just had a look in the phone book, doin't know why I didn't do that sooner (actually it was because I just found the phonebook two days ago

).
This place might be worth checking out:
Kaffeeroesterei H. Schneidedit2: Aha, this is the place I was talking about near Rotkreuzplatz:
http://www.espresso-barista.com/ highly recommended, and he also runs
barista courses!