Tampa International Airport (TPA)

https://www.tampaairport.com/

approximately 30 minutes from St Pete Beach

generally has the most options for flights

Sarasota International Airport (SRQ)

https://flysrq.com/

approximately 45 minutes from St Pete Beach

St Pete/Clearwater Airport (PIE)

https://fly2pie.com/?nocache=1750181769465

approximately 20 minutes from St Pete Beach