Where can one buy a reliable and not so expensive racing helmet?

Police Departments, hospitals, PTAs/PTOs and other organizations in your area may give them away for free to children at events to promote bike safety. You can call such a group in your area and ask.

You can check prorider.com. ProRider is a manufacturer that sells directly. Helmets may be as low as in the $5 range for organization purchase, quite a bit more for individuals but still relatively inexpensive.

Department stores (starting at $20) are generally cheaper than bike shops (often $30 and up), but bike shops can help with fit and other advice as well as offer a good selection.

Be wary of used helmets. They may have been in a crash, although signs might not be visible. Also, manufacturers recommend replacement after 5 years, though they can last much longer than that.