Yes, there is such a thing as a "good" kind of tired. There's something about being tired after a good workout, or after scrubbing the bathtub or weeding the garden (I'll have to wait for spring for that one, sadly). You get to the end of your work and you've accomplished something. This is the time that I love to work on my writing.
I've recently started revving up to write another story. Yes, another *rolls eyes*. I'm plotting this one out like I did the last and it seems to be going well, but I find that my best writing comes right after a good workout (now a days that means yoga or a nice long treadmill walk). I finish and have that "ah, I'm done I can sit down now" moment.
As soon as I do sit, all those thoughts that had been churning around in my head start to spill out. This is especially true after a couple miles of walking on the treadmill. Seriously, there nothing to do when you're walking on a treadmill but stare at the wall in front of you. I love walking outside (when it isn't 10 °F) and I find it relaxing and generally inspiring. It's also too interesting and distracting to work on a specific idea. Normally my thoughts follow this kind of pattern:
"Hmm, should I make the heroine stronger in the second act or- Ooo! Look! Was that a bird? Wait. What was I thinking about?"
But inside, that's a different story. Even if I don't feel like working on that particular story, I will, sooner or later, just to relieve the boredom. I do keep a note book next to the treadmill, but I find it's better to hold in the ideas. Then when I'm done walking I'm almost ready to burst.
Then in that wonderful state when your body is tired and your mind is itching to go, I can settle down with my note book and scribble everything I thought of while I was walking. Once you get the flow going, everything else will fall into place.