The right place to practice ballet is a place where you feel comfortable. And in order to feel comfortable, you need two different things — space and privacy.
When trying something foreign, like ballet, you need to feel totally at ease, with zero intimidation factor. So send away any snickering significant others, and consider locking out the dog, as well.
Determining how much space you need
Regarding space: At first, you don't need much. If you can lie on the floor with your limbs outstretched, and then stand upright, arms above your head, without hitting the ceiling, you've got it made.
But later, as you attempt the turns and leaps of the so-called center floor work, the demands of the space increase. You need more unobstructed room around you in all directions. A 10-x-12-foot room can keep you happy for a little while; after you graduate to more advanced movements, you may want to rent a dance studio by the hour, join a beginner ballet class, or remodel your home.
At one time or another, all dancers deal with small spaces, even in the professional world. The backstage area of the City Center Theater in New York City is so small that the wings on the left side of the stage end literally a couple of feet from a brick wall. There is barely enough room for two skinny dancers to move around in the wings during a performance.
Other considerations
As you're looking for a place to practice, consider more than just the space of the room. The space you choose should also be warm, with no drafts. Your muscles need to get warm and stay warm, even as you strip off your outer layers of clothes.
Ideally, you should also have a mirror in the room. Ballet dancers are constantly checking their technique, adjusting their alignment, and admiring their great legs. With a mirror, you can compare your own work with the figures in this book.
Also, you definitely need a music system. The control (or remote control) should be close at hand, so you can start and stop the music as needed. You also need speakers good enough so that you hear the music, not the sound of your own heavy breathing.
For a "silent" art form, ballet sure makes a lot of noise. Your feet make swishing sounds as you brush them in straight lines or half-circles, rapping sounds as you tap the floor, or smacking sounds after a leap through the air. If you have downstairs neighbors, try to be considerate of their lives. See if you can practice while they're away. Better yet, tell them what you are up to, so they don't have you investigated for suspicious behavior. Who knows — they may get so inspired by your ballet quest that they'll want to come up and join you.