Oh sunflower mom,
I'm so sorry and, as a mom whose 15 year old gal ran away for a brief period, I am sending you a warm cyber-hug. I very much hope that you know more now. But, if you are still in the dark, I imagine you are terrified for her, feeling oh-so-worried about her, all while mending your own broken heart and keeping your family afloat.
My daughter ran away for about two weeks a number of months ago. We never would have predicted that we would have found ourselves in that position. But, I think many of us on these discussion boards have thought the same thing at some point.
The situation with our daughter was different in many ways, the most important being that our daughter had her phone with her and, as a result, we had intermittent access to her location. Also, she was still attending school and, after communicating with school administration, we had adult eyes on her (at least during day hours). Very different from your situation.
At the same time, I will share the things that we did as we tried to track her whereabouts.
1) Social media, most specifically snapchat. Is your daughter active on snapchat? Do you have her passwords? Do you have a snapchat account that follows her? Or, are you close to one of her snapchat friends that follows her? Does she do snapchat 'streaks' with friends? If so, then there may be the chance that she is logging on to her snapchat account through the phone of the guy with whom she left the facility.
Snapchat has that controversial/risky 'location sharing' feature which, in this case, might help. If she has that feature on, then you can find her location and, equally important, you might be able to figure out the identity of her 'companion'.
If you have access to her snapchat account (in that you have her password), can you toggle the location feature so that it is on? Can you contact any friends that might be trustworthy, and ask them if they have seen her location through snapchat?
2) We also tracked her location through other apps and this may not work if she doesn't have her phone. For example, our daughter has a particular coffee chain app on her phone. We communicated with her during the time she was away and said that we would keep money for this coffeeshop on her app so that we knew she had access to food. The advantage of this is that this app tracks purchases with time and location (which location was visited and when).
I realize that this may not be useful. Do you have any access to communications with her? Can you tell her that she can load up an app to a phone that is accessible--and then share the username/password with her of this app with her. Tell her that she can use the app to get access to food etc.
3) We tracked purchases/locations through bank card. I imagine that you may already be trying this if your daughter bought a bank card with her.
4) We sent her messages through social media (can you communicate with her through instagram or any other social media?).
a) We told her that we weren't mad. We were concerned. Could she send a selfie of herself so that you can see her face? Can she send some sort of message/evidence to you so that you know she isn't being held against her will?
b) We told her that she could come home whenever she wanted. She wouldn't be met with anger/punishment. She could home for a brief visit to get new clothes/take a shower. Our daughter took us up on this. She came home for just a few minutes to get some clothes. It broke my heart that she left again but I'm glad she did because we could prove to her that she wouldn't be met with anger.
c) I invited her for a meal away from our house. On neutral territory.
d) We told her over and over again that she was missed. As hard and as artificial as it seemed, we tried to send non-urgent messages as well...a story about something that happened during the day that made us laugh and reminded us of her etc.
5) Do you have the password to her email address (in particular, the email address that may have been used to sign up for social media). If there is a log in to apple Id, instagram, and so on from a different device....then an email will often be sent to her email address alerting her to a new log in (and often gives the general location of the log in).
6) Her younger siblings did not know that she had run away. They just thought she was staying at a friends' houses. One of the sibling sent text messages and she replied to these messages. This has big risks, of course, and could easily have gone down a bad route. We didn't ask the sibling to send a message.
Sunflowermom...I know this is so hard...having a child whose decision making skews to the risky and dangerous, not knowing where our children are, not being able to keep them safe.
Are there people in real life who are supporting you? If so, please let them share your worry.
One thing that helped was writing to her in a journal. I would write her---about my love for her, concern, helplessness, frustration, sadness, fear...and, yes. sometimes, anger....
Please keep us updated, sunflowermom.
How are you going to pass the time while waiting for more information? I know this time period will be one of anxiety and stress for you. Sending positive thoughts to you and your family 
