FINGERS, HANDS, HEADS.  Yes.  Some artists will tattoo your fingers, hands or head.  Some will not.  Tattoo artists call these types of tattoos "JOB STOPPERS" for a reason and we generally won't do them unless you already have experience with highly visible tattoos.
INNER LIP.  No. There is a high chance that an inner lip tattoo will heal poorly and end up looking faded, blotchy or incomplete and may actually disappear over time.