Well, as you mention in your post, the obvious answer is that it absolutely had an impact, but it was more noticeable and quantifiable as the war went on and the blockade began to wear on various portions of the Confederacy. Early on (so 1861 and '62), there would have been things that were more difficult to come by, or more expensive (flour, sugar, medical supplies), as rationing for the war and pressure to contribute would have put these items at a premium. Wheat was especially prized, as was coffee, even from the beginning of the war.

Even from the earliest days, there was a general "belt tightening" that most in the Confederacy experienced, either voluntarily, or by virtue of the needs of the new Confederate War/Commissary Dept. Depending on your position within the social hierarchy (so, rich vs. poor), this would have effected you differently. Many of the most wealthy people in the Confederacy had the means to self-sustain via their farms (and pre-war food stores) up to a certain point, so they would not have felt the pinch as badly as the lower and middle classes (they weren't called that at the time, but you probably get the idea).

From 1863 onward, the Union blockade did really start to hit the Confederacy hard, though. Basic items like sewing needles, cloth, flour: things of this sort were really hard to come by. The currency devalued at such a rate that it was hard to keep up with inflation, so that buying anything even if it was in stock would have been very difficult.

The make-up of the cities that you mentioned would have been skewed towards the old, young, and female, as many of the men between 15 - 40 really were off fighting (or dead...or captured). Thus, there was a very noticeable change even early on in the war. Women took a much larger hand in the physical day-to-day doings of things in the Confederacy (working in the fields or in the households), and this was definitely a change. Of course, where you were would have made a big difference. Being in Richmond was not the same as being in Clarksville, and neither would have been similar to, say, Austin, TX. It really did vary by region, time period, etc. Early on in the war, though, what you saw when walking around town would not have been all that much different (except less men of fighting age, of course).

[Sources - Bruce Catton, 'Mr. Lincoln's Army'; Jay Winik, 'April, 1865'; James McPherson, 'Battle Cry of Freedom']