Community based treatment is, hands down, the most effective way of treating mental health problems.
Address what's causing the cutting first, and then see how much her other behavior improves before worrying about the next step.
Alternately, if you get a good therapist that thinks changing a few minor, easier behavior issues or some negative self-talk will pave the way for addressing the cutting, then if you feel good about the therapist and she has good credentials, trust her.
Someone should only be put into a facility if she is an imminent danger to themselves or others.
If you put people in facilities to try to address their problems, then when they come back into the community the environment triggers off the same problems all over again.
You, the parent, and your home, is part of that whole environment where the kid had problems. Even that serves as a trigger, even if they avoid their old friends and make new ones.
It doesn't always trigger a relapse, but it does it frequently enough to make a hard hit against the success rate of any facility.
Even if you could find the best facility that could possibly exist, community based care probably has it beat because of that environmental trigger factor.
To find a good community based program where you live, you should call county mental health. If your county does not have a separate mental health department, then call the health department. Ask your insurance company or your daughter's doctoer for a referral to a good psychiatrist or licensed clinical psychologist in your area. Try to get a practice that has more than one professional on staff, because that increases your odds that the office is familiar with whatever else is available in your area.
Julie