It's my understanding that shooting even a pellet or BB gun in town is illegal; is that correct?
I assume we are talking about Lincoln, and I think the answer is "it depends."
Generally speaking, discharge of firearms is prohibited within Lincoln, unless it falls within one of the exceptions set out in the relevant ordinance. Your Gamo is not a firearm under this ordinance because it is not a pistol, rifle, or shotgun. It is, however, a weapon that can propel a leaden or dangerous projectile, and you are prohibited by city ordinance from firing or discharging it "for the purpose of throwing or projecting missiles of any kind by any means whatsoever in such a manner as to endanger the safety of persons or property."
According to my reading of the exceptions to the prohibition on the discharge of firearms and other projectile weapons in Lincoln, shooting inside an enclosure in a manner such that the projectile never crosses an area outside that enclosure, is within the exceptions and therefore is not prohibited, assuming that you do not cause damage to persons or property. (See Lincoln Municipal Code 9.36.080 Exemptions. "The provisions of Sections 9.36.010 and 9.36.050 shall not apply to ... (c) a private building within which the instrument is fired, discharged, or operated in such a manner as to prevent the missile projected from traversing in the space outside of the private building")
In reliance on this exception, I hear that some wild-eyed firearms enthusiasts may even have basement ranges set up in their homes!
Here is the PDF of the relevant portions of Lincoln's Municipal Code:
http://www.lincoln.ne.gov/city/attorn/lmc/ti09/ch936.pdf