Best travel programs for 19-year-old female on gap year?

I would avoid EF as their tours do not offer quality experiences.

I would also caution against EF simply from groups that I have seen and talked to while traveling.

I'm not sure that I totally understand what it is that your daughter wants to do in terms of length of time and experience desired. Is she hoping to be in program for an extended period of time or is she looking for a 3 week tour?

Here is a website you might find useful
https://www.gooverseas.com/gap-year/europe

Thank you for your comments and advice!
My daughter is flexible on time, willing to partake in either short week-long trips, or trips up to a month long. My daughter has very cultured interests, and would like to visit famous sites and monuments, art museums, history museums/sites, try out local cuisine, shop, and make new friends along the way! She also enjoys walking & hiking, but isn't very interested in adventure sports like white-water rafting, cycling, etc.

Andy Steves, son of our host, runs weekend tour programs. See http://www.wsaeurope.com/blog/. I haven't heard any comments on them.

Although 70, I now have quite a bit of experience staying in hostels in Europe and U.S. After she gets her feet on the ground, she might enjoy the hostel experience, where she can even opt for private rooms in the hostel when the introvert self needs quiet. Hostels are full of students and just-out-of-college young people traveling the world. The advantage of a hostel private room over a hotel for her is that a good hostel provides very age-friendly advice and also organized tours and activities. She can meet other young people and potential friends in the lounges and at breakfast, and certainly there are conversations about other places to go and experiences to have. Of course it's super-important to read reviews of the hostels, as some are "party hostels" and others not at all, some have comfortable lounges where people actually hang out for a while and some only have super-uncomfortable chairs in public spaces, so people don't really hang out and experience chance meetings.

Just food for thought.

One to three weeks, maybe up to a month for the right program.

If she were looking for true "cultural immersion", over a longer period, I would recommend the AFS program of being an exchange student for a semester (or academic year) in a family home. My daughter spent an AFS "gap year" in Finland a few years ago, and her college was happy to defer her admission.

Is she interested in learning a language? If so, enrolling in a language program would be my suggestion. Especially in the summer, they'll be filled with others her age. I've been lucky enough to do several - one in Berlin through the Freie Universitaet, one in Dresden with the Goethe Institut, and three learning Polish at the Catholic University in Lublin (KUL). All were wonderful experiences. I went out every afternoon in Berlin, exploring the city. In Dresden, my class clicked immediately and made weekend trips to nearby German towns and a long weekend in Prague. KUL offers trips to Warsaw and Krakow, and with classmates I took weekend trips to Gdansk and Torun. I'm sure similar programs are offered in France and Italy. These programs can run from two to eight weeks, which seems to be within her time schedule. And, as nthompsan notes, once she's gotten her feet under her she might enjoy setting out on her own.

Look into Youth for Understanding and AFS for Gap Year educational & volunteer programs.

This is a very exciting time for your daughter and it is wonderful that she has an interest to travel during her gap year. With a larger amount of time available, a longer trip in Europe would certainly provide a more immersive experience. There are a variety of programs available, some meeting the criteria you provided more than others. Although she is indeed taking a gap year, the best opportunities to meet people her own age are in a study abroad program. Some universities offer these to students who are not fully enrolled. There are private programs, among them CIEE, SIT, and IES. Many European universities also offer summer programs, including University College London, University of Amsterdam, University of Copenhagen, University of Vienna, and Uppsala University in Sweden. For most of these programs, you can apply directly.

If she is willing to travel independently, staying in hostels as she travels is a great way to meet young people.
There are Facebook groups like "Girls love travel" she can join to meet other travelers in the location she is at.
Many private language programs also exist, like the Goethe institute in Germany. She could take a class or two a day, meet new people, and have most of the day free.
Helpx.net is a website for travelers who would be interested in volunteering abroad, another way to possibly meet people while traveling.
Finally, I would also suggest inquiring with a study abroad office at a university near you. They may have other great suggestions (or maybe their own programs) worth considering, even though their focus is on credit-related programs.

As others have mentioned, Andy Steves' weekend programs are a solid idea, as are the other comments regarding non-study abroad options.