By law, the max duration of a contract is now 1 year. If you know someone, try reading the newspapers, like the Luxembourger Wort. Maybe you can get something private; saves a lot of bucks.
If you decide to stay inside the country, drive around and look what area you still like.
The South/South-east is cheaper, but not as "classy" as downtown Lux.
Next to it, consider if you'll have a car at your disposal. If you'll be dependant on public transportation, you're terribly limited!