Help on finding an authentic shaolin monastary to stay

Hi! I will be travelling to China in July and would like to add a stay in a Shaolin or another buddhist monastary to my stay. I am female and would like to spend some time learing about buddhism as well as learing Tai chi. Are there any inexpensive monastaries a woman can stay in? I am travelling independently and on a very tight Budget. Do you have any tips for me?