Which airport is closest to Berlin?
BER, and there is no real alternative: Tegel closed in 2020 and terminal 5 (former Schönefeld) no longer handles commercial flights.
If BER is expensive on your dates, Leipzig/Halle (LEJ, 1h15 by ICE), Dresden (DRS, 2h) and Hamburg (HAM, 1h45) are usable — only worth it when the fare gap exceeds €60–80 per person, since the train ticket adds up.