"wish" would be a perfectly acceptable rendering of this sentence into English. It should be an acceptable solution. Again, the rigidity of what is an acceptable English translation from the Italian is a continuing flaw in this program.
"to wish," just like an English, is a different Italian verb: «desiderare» → «Puoi stare qui se desideri.». Also, "if you would like" is a different mood, the conditional, of the italian verb «volere»: «vorrei».
There's just something not very gracious or polite about that. I think "you can stay here if you wish" is preferable and should also be accepted. Having said that, the "want" version would be OK among people who knew each other very well.