We have performed low-temperature scanning tunneling microscopy measurements on single-wall carbon nanotubes that are freely suspended over a trench. The nanotubes were grown by chemical vapor deposition on a Pt substrate with predefined trenches etched into it. Atomic resolution was obtained on the freestanding portions of the nanotubes. Spatially resolved spectroscopy on the suspended portion of both metallic and semiconducting nanotubes was also achieved, showing a Coulomb-staircase behavior superimposed on the local density of states. The spacing of the Coulomb blockade peaks changed with tip position reflecting a changing tip-tube capacitance.