This seems to be a common problem. There is a thread on one of the British forums about exactly the same thing.

I had knee pain too just as you describe - in the inside of my knees. It affected my right knee more than my left. I put it down to muscular rather than anything else as I was cycling more than I'd ever done in my entire life. Sure enough, after a couple of weeks, the pain went. I don't get it anymore and I haven't adjusted my seat. My seat is at it's lowest point (I've got short legs) and my legs are almost straight when I'm pedalling so I think the height is probably about right. It'll be interesting to see what happens when I get my new bike next month.

Interestingly something I've noticed - if I don't cycle I get minor aches and pains all over, some in my back, some in my neck etc. I found this out last week when due to bad weather and other things that cropped up I only commuted once to work and had to use the car the rest of the time.

Methinks the "feel good factor" isn't just a psychological thing - it's a physical thing as well.