It's worth climbing to the top of this monument, not only to appreciate the enormity of the thing, but also to see the charmingly kitsch art nouveau propaganda mosaics in the colonnade and - most importantly - to enjoy the view from the only place where you can see the whole city centre without the panorama being disturbed by the bulk of the Vittoriano itself. At the top of the first set of stairs, two soldiers stand guard at the tomb of the milite ignoto (unknown soldier), placed here after World War I. Halfway up the terraces on the east side is the very pleasant outdoor Caffè Aracoeli.
In the bowels of the building are various spaces: the Museo Centrale del Risorgimento (entrance through unmarked open doors halfway up the steps of the monument or from via San Pietro in Carcere) has all kinds of exhibits on the 19th-century struggle to unify Italy, including the rather fancy boot worn by Giuseppe Garibaldi when he was shot in the foot in 1862, and panels (in English) explaining the key figures and events of the period. Some of the exhibitions held at the Vittoriano give access from the entrance in piazza Aracoeli to a maze of Roman and medieval tunnels extending deep beneath the monument.
The Sagrario delle Bandiere (entrance in via dei Fori Imperiali) contains standards from many Italian navy vessels. It also has a couple of torpedo boats, including a manned Maiale (Pig) torpedo. On the south-east side of the monument (entrance on via San Pietro in Carcere) is a building whose sign reads 'Museo Centrale del Risorgimento'; it does in fact provide access to the museum, but most of the spaces here are used for special exhibitions of mostly modern art. (Any exhibition advertised as held at the Complesso del Vittoriano will be here.)