I was privileged to have been in Berlin before and spent over a week there. However, if you are on a time crunch, say 2 days, here are some things you can do and see without rushing everywhere. At least, these are what I did when I had 2 days in Berlin recently.
Each day, I started touring around noon and ended around 4pm/16. If you start earlier and or end later you may be able to see more.
1. Brandenburg Tor + Holocaust Memorial (which is very close to the Tor)
2. See parts of the wall all over the city- There are memorials and information panels as well to better understand the lives of the people at the time. One area intersects with the Berlin Wall Memorial. Just follow the path. The second area is the East Side Gallery, which features the classic kissing painting.
3. Check Point Charlie
5. Parliament building
6. Berlin Cathedral
7. Check out the hipster areas and one of the numerous parks
I took some metro trips, but a lot was due to walking. A single ticket, good for U/S-bahn, tram, and bus, for 120 minutes. You can take a lot of trips in 2 hours. A day pass is valid until 3 am the next morning, but in price it’s 2 single tickets so if you ride at least twice, you break even.
I hope this helps with travel planning! This being said, if you don’t have a time crunch, try spending several days in Berlin to follow absorb the culture and, of course, if you go during a weekend, experience the nightlife (a friend of mine once went to a club at 5 am and didn’t go home till 2pm/14).