  We describe directed searches for continuous gravitational waves from sixteen
well localized candidate neutron stars assuming none of the stars has a binary
companion. The searches were directed toward fifteen supernova remnants and
Fomalhaut~b, an extrasolar planet candidate which has been suggested to be a
nearby old neutron star. Each search covered a broad band of frequencies and
first and second time derivatives. After coherently integrating spans of data
from the first Advanced LIGO observing run of 3.5--53.7 days per search,
applying data-based vetoes and discounting known instrumental artifacts, we
found no astrophysical signals. We set upper limits on intrinsic gravitational
wave strain as strict as $1\times10^{-25}$, on fiducial neutron star
ellipticity as strict as $2\times10^{-9}$, and on fiducial $r$-mode amplitude
as strict as $3\times10^{-8}$.
