Nothing or sold out at both the Opera House, Eiffel Theater and Operett Theater.
The national theater also is sold out and nothing showing at the Liszt Academy, but check back on this one as sometimes they add things without much notice https://uni.lisztacademy.hu/programmes .
You can also check the Budapest Jazz Club for updates: https://www.bjc.hu/home/ .
But a few things available at Opus Jazz https://opusjazzclub.hu/ (buy tickets and make dinner reservations separately) .
And the Comedy theater has a concert night with seats still available: https://www.vigszinhaz.hu/program.php?mid=pw9YOs0FselV7ujGT26gLN&eventid=848086 (might be easier to buy the tickets here ... but seems fewer seat choices .. https://jegymester.hu/production/10080388/comedy-theatre-vig-125-koncert/8245879 ) One thing I can promise you about the VIG, is you will be the only tourist in the audience. But its a beautiful old theater and quite famous locally .
And there is a free concert at the Hungarian House of Music: https://magyarzenehaza.com/en/occasion/times-new-roman .
Music and theater are a part of Hungarian life, so things sell quickly.