Especially during teen years, it can be difficult to have a good parent-child outing. Fortunately for both mother and child, you can plan a nice outing.

[edit] Steps

Ask your mom what she would like to do. If you would rather surprise her, ask in a subtle way, or just use your powers of observation. Try to have several options.
Think of common interests . Perhaps you both love watching soccer, or knitting, or swimming.
Suggest a day when she's free . She'll be annoyed if you interrupt work or other plans.
Plan most of the outing yourself to save her the trouble. She'll enjoy the experience more.
Behave on the outing. Make nice conversation. Use the opportunity to be genuinely engaged and listening. Your mom will appreciate your effort.