Darul Ifta Birmingham estimates the mahr of the daughters of the Prophet as £1146.28 and the minimum mahr as £23.88, based on calculating the then-current value of 10 dirhams (another estimate is given by fatwa.ca).
So if the wife doesn't want mahr, she can accept a nominal amount (and Islam Q&A says reducing it is the sunnah). However, mahr is considered compulsory for a valid nikah (IslamWeb).
Darul Iftaa Trinidad describes some alternatives to money:
A woman may ask for something other than currency, gold/silver as her Mahr, e.g. furniture or accommodation etc. if its value is equivalent or more than the minimum amount of Mahr.
Fatwa.ca cites Qur'an 4:24 (...[provided] that you seek them [in marriage] with [gifts from] your property...) in support of saying the mahr must be "wealth". I'd personally like a ring (which IslamWeb indicates is possible).
There's some uncertainty about the hajj pilgrimage being mahr, as described by IslamWeb.