I did most of my training at a towered airport in Class D airspace (KPNE). From my experience there is no "best time" (although there are times when the airspace is more empty) and for what it's worth I found it better to train when the airport was busy as it offered me the chance to practice some real world scenarios.
Running laps in the pattern when no one was around did not really build up my communication skills with the tower as they basically would just clear you for the option every time. When there were other planes in the area they might extend a leg of your pattern or have you do a 180, and these scenarios were better practice in my opinion. Crowded radio frequencies also keeps you on your toes and gets you better practice (especially if there are some similar tail numbers in the area).
You will not be upsetting operations by any means. ATC is there to handle you and frankly it's always good to practice being diverted (if that's what happens) in a busy airspace so you will know how to handle it when you get out on your own missions.
Class C/D space airports generally run a lot of large private traffic and some scheduled carriers. I found that KPNE and KABE (if I wanted to practice in class C) were heavier later in the day and early in the morning as would be logically expected. But to be honest there were plenty of times a bunch of planes would come in all at once mid day and it would be quiet the rest of the day.
If you are a student pilot (you did not say in your question) you can identify yourself as such when entering the airspace and when getting on with the tower. In most cases it will make them a bit more forgiving if you ask for an instruction repeat or don't understand something.