I don't think the fitness routine of someone with hypothyroidism really differs from someone who doesn't have the condition. In general, we recommend 3-5 days of cardio each week for around 30 minutes, as well as strength training 2-3 times per week.
Hope that helps,
"You may have a fresh start any moment you choose, for this thing that we call "failure" is not the falling down but the staying down." Mary Pickford