I've been to the Nike Amherst tennis camp each year for the past three years, so I kind of know the drill. If you're going solo, I'd suggest going during a "singles" week. Tennis camp is like Noah's Ark. Campers often come in twos ... except during "singles" week. If that's not possible, don't worry. Everyone is pretty friendly and approachable. It's just that couples are more likely to form insular units.
When you register, you can actually request a particular instructor for your private lessons. You get a 1/2-hour private lesson in the morning, before the drills. Reiny (the director), Maureen, Noah, and Errol are the most experienced instructors. Most returning campers will request Reiny. So there's only a slim chance you'll get him, but the others are quite good. Noah is good if you're an advanced player. If you don't request an instructor, one will be assigned. And that's fine.
My only real advice to maximizing the camp experience is to play as much as possible ... and that especially includes the evening round robin doubles. After five/six hours of tennis, you may be tempted to opt out of round robins. Don't. Figure on catching a second wind. You need to get used to competing. And they're friendly matches. You'll probably win as many as you lose. The only thing frowned upon is taking winning and losing too seriously. You're there to improve ... and that means getting beat once in while. You'll be playing people you've never played before and will probably never see again. So learn to adjust your game.
Amherst is a very nice little college town. Amherst College, UMASS, and Hampshire are all within six miles of each other. Smith College is in nearby Northampton, and that's a very pleasant little city. Mt. Holyoke College is also about 10 miles away ... in South Hadley.
Soon after you arrive (and finding where to register may be tricky. There are several camps -- soccer, softball, junior tennis -- going on at once. Look for signs.), you'll be given an audition, and a chance to play doubles. The next morning (after your first private lesson), you'll be assigned to a group of four (no more than four) of the same skill level. Reiny is very good at determining these levels. The groups will be adjusted or not. You'll move from court to court (every half hour), instructor to instructor ... working on ground strokes, volleys & overheads, serves ... drills and competitive situations. The time will fly. Bring lots of shirts. I went through four shirt changes a day (although there is a laundromat in the dorm).
You can buy extra private lessons. $30 a half hour. You might want to get a lesson with Reiny. He's a terrific instructor.