Another suggestion
First, I agree with the others that HAL will offer your mother a better experience than NCL. I've cruised on most of the major lines, and NCL is the only one I wouldn't even consider. [It took them eight months -- eight months! --to refund a refundable deposit years ago, and that formed a lasting impression].
Another option to consider, if the dates will work, is the Celebrity CENTURY, with 10-night RT cruises from Barcelona that visit Marseilles, Nice, Livorno (Florence), Rome, Corsica, Valencia, and Gibraltar. I sailed on the Century in the Med eight years ago, and I still consider it (and its sister ships) some of the most beautiful in the mid-range category. Especially the grand wood-paneled dining room. In my view, the food on Celebrity is at least equal to HAL, and the service is just as good, though the entertainment may be a half-step below (depending on one's personal taste, of course).
According to Travelocity, an inside cabin on the Century costs $1,229 on 10/12, $1,179 on 11/2, and $949 on 11/23 -- extremely cheap for ten nights in the Med, especially on a ship of this quality. (Celebrity just spent $55 million or so refurbishing the Century.) Outside cabins run $2,149, $1,369*, and $1,249 for those dates. (*with a $100 pp discount available on this date).
That's the best deal I see at this time, but check the big sites like Travelocity and Expedia, and the "bargains" section on cruisecritic.com. and other discount sites on a regular basis.