Berlin punishes the unplanned day. The city is vast, the sights are scattered across it, and the difference between a good twenty-four hours and a frustrating one is almost entirely about the order you do things in. Two travellers can work from exactly the same list, and one will finish it calmly by eight in the evening while the other is still standing on a platform at nine, having spent two hours of their single day underground.
This route runs broadly west to east, keeps every transit hop short, and asks you to give up three things you probably wanted to do. That last part is the important one.
Before you arrive: two bookings and one ticket
Register for the Reichstag dome online. Access is free, but it requires advance registration through the Bundestag's visitor service, and the booking window opens on a rolling basis roughly three months ahead. In high summer the morning slots are typically gone within days of release; in winter two or three weeks of notice is usually enough. Book the earliest slot offered — the dome is calmest before the middle of the morning, and starting there sets up everything that follows. Bring the identity document you registered with, because the confirmation is issued in your name and cannot be transferred.
If you have missed the window there is a walk-up route: a service point near the building issues any places still free, but generally only a couple of hours ahead of the slot itself, which means queuing early and building your morning around an answer you do not yet have. Check the parliament's own site before you travel, too. The dome closes for cleaning and maintenance for a week or two most years, usually in autumn, and the roof terrace stays open when it does.
The second booking is your evening viewpoint, which we will come to. The one ticket is transit: buy a 24-hour pass for the two central zones, which costs somewhere around EUR 11 at the time of writing. A single journey is roughly a third of that and you will make four or five, so the pass pays for itself before lunch and, more usefully, removes every small decision about whether a given hop is worth the fare. If you are arriving from the airport you need the wider zone that includes it; inside the city the central pair is all you need.