What is wrong in visiting a shrine other than holy Prophet's (PBUH)?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.

Visiting the graves and graveyards is not wrong if done according to the purpose for which it was legislated. That purpose is exhortation as well as introspection and supplication for those who are dead, and if all this is done according to the Sharee’ah rules in this matter. Imaam Muslim narrated from the Hadeeth of Buraydah that the Prophet Muhammad, sallallaahu ‘alayhi wa sallam, said: “I had told you before not to visit graves, but now you should visit them.”

Abu Dawood and An-Nasaa’i narrated the addition: “…for indeed they remind you of the Hereafter,” to this Hadeeth, while Al-Haakim narrated the addition: “…for it softens the heart and fills the eyes with tears; but do not utter any bad words there.” He also added from the Hadeeth of Ibn Mas’ood : "They make one renounce worldly pleasures." Muslim also narrated from the Hadeeth of Abu Hurayrah : "They remind (one) of death." So, whoever visits graves for the purposes mentioned in the Hadeeth and the like and does not say or do any evil such as becoming a polytheist due to taking someone or something as a partner to Allaah in words or deeds or appealing for help from any but Allaah or weeping loudly or complaining about Allaah’s destiny, may do so, and his visit would be lawful. The person should also avoid things like wiping himself on the grave, or circumambulate it. If the person does what is legislated and forbids what is evil, then his visit would be permissible.

Allaah Knows best.