There are a total of 240 nuke symbols in the game:
8 levels, 3 parts each, with 10 nukes in each part.
So you don't have to worry about finding every single one in every level. I got this near the end of level 6, part 3, just by picking up ones that I stumbled across. I never went out of my way to find them.
Though it is a good idea to try to get all 10 in each level as every time you do, your max health and ammo increase a bit. The game is still plenty doable with out the upgrades, but every little bit is nice.
EDIT: Just noticed d3r1v3d has already posted a link to a guide for all symbols in the forum. Duke Nukem: Manhattan Project - Nuke Locations
In case you want them all.