Near the station is the Ibis hotel. https://www.accorhotels.com/gb/hotel-6510-ibis-basel-bahnhof/index.shtml
I've stayed there. Very convenient and I heard no noise whatsoever. Simple and predictable, with nice staff, and at the junction of two tram lines. I don't know if their definition of moderate meets your definition. For a random date in May (no knowledge of the real date) - the 8 and 9, the quote is (the first figure is no Accor membership, the second with; free membership easy to get)
ADVANCE SAVER RATE
Cannot be cancelled or refunded
240 CHF 228 CHF
Members' rate
VAT included. Taxes not included : 16 CHF
FLEXIBLE RATE
Cancel free of charge until May 8th 14:00
282 CHF 267 ,90 CHF
Members' rate
VAT included. Taxes not included : 16 CHF
ADVANCE SAVER - BED AND BREAKFAST
Cannot be cancelled or refunded
Breakfast included
296 CHF 281,20 CHF
Members' rate
VAT included. Taxes not included : 16 CHF
IBIS SPECIAL EVENT RATE
Cannot be cancelled or refunded
282 CHF
VAT included. Taxes not included : 16 CHF
FLEXIBLE RATE - BED AND BREAKFAST
Cancel free of charge until May 8th 14:00
Breakfast included
338 CHF 321,10 CHF
Members' rate
VAT included. Taxes not included : 16 CHF