Is it okay to go to a local clinic for a lifting procedure?

I am planning to get a lifting procedure. I am wondering if it is okay to get it done at a local clinic, even if it isn't a large dermatology clinic or a famous one. I've noticed a significant price difference, so I would like to know if there is a big difference in terms of results or safety. I would also like to hear the experiences of those who have actually received the procedure at a local clinic.