Admiral -
I trust you've already read the Vicksburg piece ('The Beleaguered City') in Shelby Foote's Civil War Narrative? 'The Beleaguered City' was also published by itself as a separate book (as you probably already know).
I just got a new book on Vicksburg, but I haven't read it yet. It's called 'Vicksburg is the Key' (authors William L. Shea and Terrence J. Winschel; University of Nebraska Press; 2003). Obviously, I can't attest to the quality of it yet, but it looks pretty good. A brief excerpt from the Introduction:
"As William L. Shea and Terrence J. Winschel skillfully demonstrate, the Vicksburg Campaign, which was really a series of separate operations, was the longest and most complex of any during the Civil War. [.....] By the summer of 1862 the Confederate defensive position at Vicksburg had become a focus of Union operations; Northern political and military leaders understood the significance of cutting the Confederacy in half. [.....] The Vicksburg Campaign was a critical stage in Ulysses S. Grant's development as a military leader. As he evolved from soldier to general, he learned to anticipate difficulties and adjust his plans as situations developed. [.....] The campaign was also one of the few operations that successfully combined army and navy resources. Perhaps one of the most dramatic events was Adm. David D. Porter's run past the Vicksburg batteries in order to ferry Union infantrymen across the river below the city. Grant's bold decision to move inland remains one of the great feats of the war - in seventeen days the army marched two hundred miles, fought five battles, and pushed the Confederates into their defensive works. [.....] Strategically Union control of the Mississippi separated Arkansas, Louisiana, and Texas from the other eight Confederate states; an accomplishment of immeasurable consequences." [Vicksburg is the Key; Introduction]
I'll be anxious to see what other people recommend as I find Vicksburg to be the greatest campaign of the entire war. Indeed, Vicksburg is nothing short of stunning.