A substitue for "man" could be "dich" or "Sie" or "euch" etc., but I would just throw it away. "Man" is wrong here anyway, you cannot use it with prepositions. It may be only nominativ singular.
"Wohnung" is the place where you permanently live. It's never used for a temporary accomodation like a hotel, hostel or like that. A correct word might be "Hotel", "Zimmer" or simply "Übernachtung".
"Damit" is not correct too. It has a different meaning ("so that, in order that"). The sentence "damit man Geld sparen kann" would mean that you can only save money if you do something what was mentioned in other part. Example: "Ich lerne Deutsch, damit ich Geld sparen kann" - "I learn German to save money".
All in all: Ein anderer Nutzen eine Fremdsprache zu lernen ist, dass man Geld sparen kann, weil man für die Übernachtung (auf Reisen) nicht zahlen muss.