How can I find out the best time to practice within towered airspace?
Simplest answer: Call the tower. Or ask instructors/schools in the area if the controllers care when you arrive and want to practice. Usually if you arrive during the busiest time, you'll likely be accommodated as best as they can, but there's a chance you could be told to just do a full-stop taxi-back operation if that helps out or told to go fly around elsewhere for a bit.

It depends on what airport you're thinking about going to. If you want to go to ATL, well, you'll be vectored in a gap, and told go as fast as you can for as long as you can, and be told to land(or if you go around, expect a long delay to find a new gap). If it's just a general aviation airport, anytime is fine.