As Bill commented, 'alongside' suggests something like ships. It would usually refer to a static situation. Apart from 'near' possibly being somewhere other than beside, it also sounds awkward to me. That sentence would be more natural without the 'to'.

You could use any of them, but there are some slight differences. Near would just mean close by, so that could by beside, or behind, or in front of you. I'd only ask someone to walk near me if I wanted them to walk closer than they currently are. Next to me and beside me are both the same, and sound natural. Alongside me technically means the same as beside, but it sounds a little off in this context. As Bill mentions, it's often used for ships or boats, but not often for people.

Well "near" could also be in front or behind me. "Alongside" sort of works but it might be normally used for ships being alongside each other.