Where is a neuroma excision usually done? At a hospital?

Depends. While done as an outpatient procedure, whether your surgery is at a hospital or ambulatory surgery center depends on many factors: where your physician prefers to perform surgery, where he or she is credentialed, and the types of facilities available in your area. Additionally, many physicians operate at both types of facilities but may select the location on or availability or type of case.
Possibly. Many doctors can take neuromas out in the office. Depends on whether the doctor has the equipment or not.