As a sometime native I'm not always best placed to advise on hotel-type stuff as I haven't had to book a hotel here for over 15 years. My two tips would be
1. See if you can book the flight and hotel together with British Airways. Goat of this parish did this a while ago and I don't believe you could get better value (he was in a hotel near Zoo and just off the Ku'damm).
2. The local Swedish church offers basic but cheap Pension-type accommodation (circa €50 a night) - we've put a few people in there in the past but I'd say there's a significant risk that some bloody marathan runner has already gazzumped you. Ring them up - they probably speak better English than I do.
https://www.svenskakyrkan.se/berlin
If I have any better ideas I'll update the thread.
On an unrelated note how are you getting on with that West End Sowan with the arabic numbers? If you don't like it I might want it back
.