Thanks everyone for the suggestions. Some I eliminated because they were too far away, or too expensive, or there was too much contrast between the good and bad reviews of the place (Rudy's). I also didn't like that Sugarcomb charges a different amount for women's and men's cuts. If they want to make a distinction it should be between short and long hair.
So the winner is . . .
Lisa, at Stardust Salon, 7220 Linden Ave.
She did exactly what I asked for, and the price was very reasonable: $28. for short hair. I recommend her.
But here's another question. I didn't tip her, and now I'm wondering if I should have. I thought that when people own their salons they get to set the price at whatever they want, so there's no tipping. If they are just renting the chair and therefore have to pay part of their take to the owner, then there's a reason to tip.