Do you have some other pedals to put on it and see if the click goes away? I had a click that I felt more than I heard one time. It was in my right pedal and would happen when I was accelerating at a moderate power and would occur when the right crank was about the 3 - 4 o'clock position when viewed from the right.
It turned out to be the pedal bearings just needed to be adjusted. The bearings and races in my Shimano PD-A520's are very tiny. So even when out of adjustment there is virtually no visually perceptible play that can be seen. So don't just ignore doing something about the pedals because you can't see anything wrong.
Pedals may not be your issue, but for what you've described they will be the first thing I change out just to see. Then if that turns out to be the case, then you can clean, lube and adjust the old pedals and have a spare set to put on the shelf. Everyone should have shelves of spare bike parts taking up space! <not><grin>