Is it permissible to visit the graves of saints and the righteous – such as visiting the the grave of the Prophet, peace be upon him – with the intention that they were righteous and not to venerate them, or is that one of the devil's gateways?

Visiting the graves of awliya (saints) and righteous people can be permissible if it adheres to the controls of Sharia and achieves its objectives; otherwise, it is prohibited. The visitor must denounce forbidden acts and innovations (bid'ah). If unable to do so, he must leave the place.