Help converting ECI to RA DEC
Assuming you are calling cEci and have the units and sign conventions correct (longitudes are notoriously inconsistent as to which way is positive) then you should be able to calculate it almost as you have as:

distance = sqrt(x*x + y*y + z*z)
RA = atan2(y/x)
# Normalize right ascension into the 0..2*PI range
if ( RA &lt; 0. ) 
  RA += PI + PI
Dec = asin(z/distance)
# Convert radians to hms and or degrees to taste


This code was taken from Bill Gray's sat_code, specifically observe.cpp. Other bits of that code handle the conversion from a latitude, longitude, height (geodetic coordinates) to a X,Y,Z vector from the Earth center to the observing site (geocentric co-ordinates) and then the rotation by the Local Mean Sidereal Time (site longitude + GMST, where GMST is the Greenwich Mean Sidereal Time) and then the 2 vectors (Geocenter->Site and Geocenter->Sattelite) are added. However it looks cEci already has this as I see references to the flattening factor and LMST.

One thing to note with TLEs is they are not a very good representation of the satellite motion/orbit over long periods of times. You should make sure your TLEs are up-to-date or use something like SGP4 to apply the perturbations and update the TLEs.