Where is the best place to have eyelid surgery--outpatient center or hospital or?

Depends. It depends upon the local standards and where the surgeon feels comfortable in performing the procedure safely. If it is done in an office setting, make sure that the facility meets state standards and has the proper equipment and monitors.
Both good. The optimal place to have surgery is where your surgeon is comfortable and feels you can get the best care.
Outpatient center. Most physicians perform cosmetic and functional eyelid surgery in an outpatient setting (private office versus asc or ambulatory surgery center). Baseline health issues may require the surgery to be done in an asc or very rarely a hospital. Reasons to avoid the hospital include likely higher facility cost and potential exposure to hospital infections.
Eye surgery location. Eyelid surgery is almost always an outpatient procedure and an outpatient surgical center is usually a cheaper route. Both should give equally high quality care. The operating surgeon is the key to the best outcome.