How many MM is the circumference of my 700x23 tires?

You should absolutely measure!  I used one of the standard measurements for a while and then I noticed once that my computer and mapmyride.com differed by a full km over 60k.  So I measured the tire and when I used the new number, it matched up with mapmyride much better.

Will def do this.

I doubt difference quoted by the previous poster makes much of a difference in actual mileage, this is what I have read in the past to get an accurate measure. FWIW I have probably done this once, years ago and probably 6 or 7 bicycles ago. I just use the chart the computer comes with and ride now. I do know my Cateye wireless tends to be a tad generous on the miles but I don't believe it is seriously compromising my training or anything.

Being off a few millimeters makes very little difference -- about one part in a thousand per mile.  So if you're high or low by, say, 3 millimeters, then for every 1000 miles you thought you rode, you actually rode 999 ('roughly').

I'll venture to say that this difference makes no difference at all in training or in racing.

The fine print:

Suppose OP reports 2096 (the default on my computer) as the diameter.  Then the computer says that every revolution is 0.001302394 of a mile (assuming it even works to that precision), which means it takes (according to the computer) 767.81680505284883 revolutions to make a mile.  Suppose the actual diameter is 2093.  Then the computer says that every revolution is 0.0013005299 of a mile, for 768.91734669076044 revolutions per mile.  The difference is pretty darned close to 1.1 revolutions, or a little more than a thousandth of a mile.