We present the results of a directed search for continuous gravitational
waves from unknown, isolated neutron stars in the Galactic Center region,
performed on two years of data from LIGO's fifth science run from two LIGO
detectors. The search uses a semi-coherent approach, analyzing coherently 630
segments, each spanning 11.5 hours, and then incoherently combining the results
of the single segments. It covers gravitational wave frequencies in a range
from 78 to 496 Hz and a frequency-dependent range of first order spindown
values down to -7.86 x 10^-8 Hz/s at the highest frequency. No gravitational
waves were detected. We place 90% confidence upper limits on the gravitational
wave amplitude of sources at the Galactic Center. Placing 90% confidence upper
limits on the gravitational wave amplitude of sources at the Galactic Center,
we reach ~3.35x10^-25 for frequencies near 150 Hz. These upper limits are the
most constraining to date for a large-parameter-space search for continuous
gravitational wave signals.