If you go to the new Berlin Hbf, ICEs from the deep level (Tief) platforms stop within 10km or so in the suburbs at Gesundbrunnen in the north (trains from Hannover direction terminate there after reversing at Hbf), or rather more frequently at Südkreuz (Leipzig/Halle direction).
Both stations are on the Ringbahn in Zone A.
Hannover trains also stop at Spandau which is a bit further out in Zone B.
I think Berlin Day zonal tickets are valid, but not entirely sure.
Generally DB likes to keep local passengers off long distance trains.
You won't get up any significant speed on these legs, of course.
IC/EC trains towards Dresden and Hamburg also use these routes, but are not usually ICEs.