All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Islamic Sharee'ah places emphasis on honoring a neighbor, being kind with him and abstaining from any act that could harm him. Allah Says (what means): {Worship Allah and associate nothing with Him, and to parents do good, and to relatives, orphans, the needy, the near neighbor, the neighbor farther away,…} [Quran 4:36]
The Prophet said: “Jibreel (Gabriel) kept recommending me to treat the neighbor with kindness until I thought that he would assign a share of inheritance to him (i.e. make the neighbor an heir of his neighbor).’” [Al-Bukhari and Muslim]
There are many Ahadeeth proving the need to be good with a neighbor.
Know that the kind treatment should be for the sake of Allah not for any personal benefit. If one intends only the worldly benefits through his good treatment with his neighbor then he will not get any reward in Hereafter.
The Prophet said: “Indeed, actions are judged according to their intentions and every person will get the reward of what he has intended. …” [Al-Bukhari and Muslim]
Therefore, you should maintain good ties with your neighbors for the sake of Allah even if they are not good with you. Know that the rights of a neighbor are greater than the worldly benefits. So, fulfilling those rights strengthens the ties of brotherhood and increases the love and affection among Muslims that are sought after in Islamic Sharee'ah.
We should show mercy, sympathy and good conduct to a neighbor even if he is a non-Muslim to make him interested in Islam and to prove the good conduct of Islamic Sharee'ah.
Allah knows best.