There's a revive-spring and well-spring at the last level of Eureka, but that's about it. No inns, no springs in the Crystal Tower or the World of Darkness. Preparation is the key to victory here. The last section of FF III is brutal, no denying there. My personal suggestion is to not go in until you're somewhere between lv 55 to 60. Good place to grind is Bahamut's cave, relatively easy enemies that give a good deal of exp, and you can go to the Invincible outside to rest up if needed. Don't forget to switch every one to Black Belts (the monk with the cape) when grinding, they have the highest HP gain upon lvl up. Stock up on high potions if you can. Once you're lvl 60, Eureka and the Crystal Tower shouldn't pose any problem anymore. Go raid Eureka first then. Pick up the new jobs, the best weapons, everything you need. I would then personally suggest to make your way back through the ancients maze to the Invincible to restock any healing items you used in Eureka. Then go back and finally tackle the Crystal Tower. If you want it easier, then definately use Ninjas and Sages once you have them, they pack a serious punch in the NES version. Having two healers is not a luxury, either. Try and conserve MP for the boss battles, if you can. Try to use healing items instead whenever possible (those high potions I recommended). Any elixers you have should be saved for the World of Darkness, as they're your only way of restoring MP there.
The final dungeons of FF III are the only part of the game where I agree that the game went overboard in terms of brutality. Believe it or not, the developers back in the day wanted to add a save-point between the Crystal Tower and World of darkness, but gamers complained it made the game too easy.