Paris sounds like a city that I could enjoy.

Paris sounds like a city that I could enjoy.
我们老师说that的删去与否都无所谓,她说在这里面that不作成分.但是我觉得很明显that定的先行词city在后面的从句中充当enjoy的宾语,虽然that删了也讲得通,但是我认为老师的后半句话明显是错误的呀!
分析一下这句话.
问题都没有回答到点子上啊.that在这是做enjoy的宾语吗?