Responding to herenow's question about knowing when a fit will be "good enough," I don't think there is any way to be certain. Our twins are also 11, finishing elementary school and will enter middle school in the fall. Our fall back has always been to give ourselves permission to change our minds.
Dd and ds have spent the past six years in public schools. There are two private (K-8) schools in the area which are potentially reasonable, if not perfect, matches. Given the trade-offs, we went for the cheaper option, but always maintained a school fund so that we could switch to a private if the public school didn't work out. Dd is hg+ and ds is not far behind, and I felt pretty certain we would pull them from the public schools at some point. Although the public school is not perfect either, we've been able to make it work for us, and the kids are content and learning. (Every year about this time I total up how much we've saved on tuition - it has all gone into a college fund!) So despite some reservations about the local public middle school for next year, we've decided again to give it a try.
On the plus side for the public middle school is that it is a big school that will have lots of very bright kids (compared to the elementary and the privates). Statistics are in our favor with the large student body, and the school draws from an area with many high-achieving parents. One result is that there are various teams that compete very well on the state and national level, so lots of those kind of opportunities. They also offer math classes up through alg. 2/trig. so our kids will likely not have to go off site for math by the time they graduate.
The downside is that in addition to the bright kids, there will be many kids who are less capable and/or just don't want to be there. The district has a tradition of inclusiveness, with the apparent result of teaching to the lowest common denominator in some cases. So, class placement will be a key variable. Also, both of my kids are pretty creative and I can see that quality being exercised/nurtured more in a small private.
Another consideration for us is our kids. They have been happy at their elementary and view the public middle as "their" school, even before attending. I recently showed the kids a flyer we got in the mail advertising one of the privates, and the reaction was not a positive one. Even though their reactions were emotional rather than reasoned, it is still a consideration. If I had been totally sold on the privates, I would have worked harder to convince the kids of their merits, but since we were ambivalent, hearing the kids' opinions was a turning point in the decision making.
But once our kids start the public middle school, we still reserve the right to change our minds - just knowing we can change our minds eases the anxiety for me.