There are plenty of hotels, hostels and Airbnb-s in the area of the Budapest Music Center, but here are three of the closest options to suggest for accommodation (for different budgets):

• Meininger Hotel Budapest - Great Market Hall (1 min walk, different room categories for all budgets)
https://www.meininger-hotels.com/en/hotels/budapest/budapest-great-market-hall/

• Maverick Urban Lodge - Lónyay Street (budget option, hostel, 5 min walk)
https://mavericklodges.com/en/urban-lodge-budapest-hostel

• Ibis Hotel Centrum Budapest - Ráday Street (standard hotel, 7 min walk)
https://all.accor.com/hotel/2078/index.en.shtml?utm_campaign=seo+maps&utm_medium=seo+maps&utm_source=google+Maps