To reach the campus you can use the guidelines given in the link.
The METU Guest House is the closest lodging as it is inside the campus but there are several other hotels nearby (10-15 mins to campus). Some of them are Holiday Inn Cukurambar, Four Points Express By Sheraton Cukurambar, Bilkent Hotel & Conference Center.
When booking hotels, either pick ones closest to the campus, or closest to a metro station. There is a train to METU (ODTU) campus from the city center.
Websites such as expedia.com, hotels.com give more discounts to those traveling from outside of Turkey.
Guest house reservations: https://misafirhane.metu.edu.tr/rezervasyon?lang=en (please let us know if you are having trouble reserving at the guest house)
Here's the link for Campus map: https://map.metu.edu.tr/
METU Guest House (inside the campus)
Bilkent Hotel
Holiday Inn Cukurambar