This is from a user named Free Northman on westeros.org
He is very pro-North, as you can see and Ran (Elio, he works with GRRM) stated his numbers are a little too high. That's for the North. So anything from 35-40,000 from the North seems plausible.
The general consensus among the forum users who discuss military is -
Dorne - 20-25,000 (Quentyn says 50,000, but we learn from Doran himself that that number is an exaggeration to make Dorne seem stronger than it really is. Also, Doran says Dorne is the weakest of the Seven Kingdoms minus the Iron Islands).
Stormlands - 30,000 Max (Ran said GRRM doesn't think much of the Stormland's military might. All we know is that Renly had 20,000 Stormlanders in his army).
Riverlands - 25,000-30,000 (Most users agree that as a fertile and densely populated region, the Riverlands should be able to gather a lot of men. Edmure originally sends 4,000 to the Golden Tooth and was training 16,000 outside Riverrun. Later on, he rallies 13,000 more men to repulse Tywin at the Fords, keep in mind this is also after sending men back with their lords to try and stop Clegane's raids).
Westerlands - 45,000 Max (Jaime had 15,000. Tywin had 20,000. 4,000 men managed to retreat from Riverrun and helped form Stafford's army which is a speculated 10,000 men after joining strength. We then learn that Daven was trying to reform another host to replace his father's).
The Reach - 100,000+. (Renly had 60,000 of them in his army. Mace had another 10,000 at Highgarden and Lord Leyton Hightower still hadn't committed most of his men if I remember correctly. Plus the Arbor fleet and that number goes over 100,000).
The Vale - We don't have much info on this region but most users tend to speculate that around 30,000 is a good number from what we hear.
The North - As above around 35-45,000 men.
The Iron Isles - Including their navy, most people seem to estimate 25k as the absolute maximum as the Iron Islands seem to have a warrior culture of sorts meaning there are more fighting men. Plus, "they do not sow".
That should hopefully clear up some numbers. Whilst most of them won't be correct, I'd say at least all of them are within 5,000 of the actual number.
But as you can see, the only region the Ironborn can match "man for man" is Dorne really, and Dorne happens to be the most difficult region to conquer.