I went to a boarding school for my four years of high school. I am so thankful I did. I was an only child, the "miracle baby." But because of that, my parents wanted the best for me. We lived in a small hick town where the high schools were awful. I went to a beautiful, all-girls boarding school on the central coast. The classes were challenging, and there I met the girls who would become the sisters I never had. To this day, more than 20 years after our graduation, my classmates and I are all still like sisters. I think I was actually closer to my parents in high school than I ever would have been if I'd stayed home. I spoke to them at least once per week. I told them everything about my life (yes, the first kisses, first dates, all of it). I wrote them letters. I was thrilled when it was time to come home on vacation, and helped out around the house. I was able to enjoy my parents as people, not just as parents, because we didn't have much conflict (if any). And when I was away from them at boarding school, I had the autonomy that most teenagers crave - yet I also had responsibility. I had to balance my checkbook, do my own laundry, manage to get my dry cleaning sent off, remember family birthdays, wake myself up on time, get myself in to my professors if I needed extra help... needing to manage myself made me appreciate my parents soooo much more, but yet I also felt a sense of accomplishment for what I was able to do, standing on my own two feet. There are many caring adults at any good boarding school. We had teacher families who lived in apartments adjoining our dorms, so several times per week, these families would invite students to have dinner with them (and teachers who didn't live on campus would attend dinners in the dining room, and sit at the tables with us, so we had some really interesting conversations over dinner!). We also had nuns who lived in/near the dorms, and they were a great source of advice, comfort, and yes, discipline.
Best of all, I had the finest education imaginable. I had no trouble being accepted early admission into an Ivy League school, and once there, had no trouble keeping up (I graduated in just over 3 years). Many of my college friends who had gone to public schools (even "good" public schools) had a lot of trouble in college. I wasn't homesick, I was able to keep myself on track, and I knew how to manage my time, balance my checkbook, and pay my bills on time. I have boarding school to thank for all of that.
Now, that isn't to say that boarding school is for everyone. I think you would only want to send a child who is fairly mature, intelligent, and motivated. I will say that my daughters are at summer camp right now at the boarding school I went to, and both of them are so excited to head off to boarding school themselves when the time comes. I really feel it was such a broadening experience that helped me to become the person I am today. I'm so grateful my parents could see past their own needs and give me exactly what I needed at that moment in my life. I would just encourage you to look past the "smart, socially awkward" label and really look at what your daughter could gain from this. (By the way, I was the social chair of my very popular sorority in college, so I personally think you're dead wrong on the "socially awkward" judgment! ;)