How to precisely set many camera positions for rendering?

Use 'View Navigation (Walk/Fly)' mode while in Camera view - this allows you to navigate the camera as if in a 'first person' game using the keys Q (down), E (up), A (left), D (right), W (forward), S (backward), as well as using the mouse to "look around". Other keys are shown in the status bar at the bottom of the window while in Walk/Fly mode (such as Shift for 'fast' mode).

Walk/Fly mode is activated by pressing the shortcut Shift+` or pressing F3 and typing part of the description (eg, 'walk').

Note that you can use this mode even when not viewing the scene in 'camera view' (in which case it only moves your current view of the scene) but when in 'camera view' the navigation also relocates the camera to follow your view.

Set the camera (relatively) where you want it with CTRL + ALT + NUM0, then make sure the camera is selected (it doesn't matter if you exit the view). Then, re-enter camera view mode with NUM0. Press N to bring up the transform toolbox, and you can fine tune it from there. Either drag the sliders, increment with the arrows, or enter number values.