Toledo is to the south and at least a full-day destination. Many of us have been pleased to spend multiple nights there.
Segovia, I feel, is easier to treat as a day-trip, though I spent some nights there as well (making one day-trip away from Segovia).
To my mind, Avila is not much more than a wall and is skippable. I'd rather spend my time in Segovia without having to rush, but Avila (west) is in the same general direction as Segovia (northwest).
I'm not sure what you mean by "sign up". Do you mean you want to take tours? I have no idea how early you would need to book those. I just used public transportation. Both Toledo and Segovia have fast rail service (AVE/ALVIA/AVANT) that gets you there in about 30 minutes. Travel time by bus will be at least twice as long, plus you'll probably lose some additional time with the loading and unloading process.
However, if it is a must for you to see both Segovia and Avila, and you need to do that on the same day, I suppose a tour might work out better. The link between them is by bus (not especially fast), and I imagine those buses don't run terribly often.
Another great day-trip from Madrid is Cuenca, but that works only if you take one of the fast trains, and those tickets can get rather pricey (for a day-trip) if you don't snag discounted promo tickets early on.