There are two ranges at USNA but access to them is pretty limited.
The regular pistol/rifle range across the river at NSA Annapolis is an outdoor range that is used mostly during Plebe Summer for initial pistol and rifle quals. During the Ac year, the High Power Rifle team uses it during the week for practice.
There is an indoor rifle range located in the basement of Bancroft Hall. However, it is solely reserved for air rifle/small bore shooting by the Navy Rifle team.
As far as I know, midshipmen not on these teams do not have any regular access to these ranges.