You can recycle old towels alongside other types of waste textiles, fabrics, and clothing as they’re generally made from similar fibres. It’s important you ensure they’re clean and dry to avoid introducing any contaminants. Otherwise, throw them into a textile bin and they’ll be processed and recycled in the same way as other textiles.
With old paper towels these normally go in with general waste. This is because they’re made from fibres that are too small to be of use when recycling. Used paper towels may be wet and contaminated so can’t usually go in with your dry mixed recycling.