Where is the best place to look for monthly temperature and precipitation data for Hurghada and Qosseir and the area in between these two stations?

Both the GHCN and GCPS datasets have data for these stations.

http://ingrid.ldeo.columbia.edu/SOURCES/.NOAA/.NCDC/.GHCN/.v2/
http://ingrid.ldeo.columbia.edu/SOURCES/.NOAA/.NCDC/.GHCN/.v2beta/
http://ingrid.ldeo.columbia.edu/SOURCES/.NOAA/.NCDC/.GCPS/.MONTHLY/

Go the "Searches" link on any of these pages and enter your desired station in the search table in the "Name" column. If you have trouble finding other stations in this area, then you may want to look at the gridded GCPS dataset:

http://ingrid.ldeo.columbia.edu/SOURCES/.NOAA/.NCDC/.GCPS/.MONTHLY/.GRIDDED/

You can use the same search with lat/lon specifications.