An alternate title for this thread would be: "Reasons You Should Read the Vampire Chronicles if You Haven't Already Done So"
A vampire is mentally the same person, more or less, as they were when they turned (excluding vampires that are made/born under duress or other circumstances that may lead to insanity, depending on which mythos you look at).
A "good" person can be made to do "evil" things, and if that person does those things enough times for a long enough period, they're likely to become accustomed to it and their "good" resolve will crumble away a bit more each time, until that person is "evil."
Likewise, an "evil" person can be made to see how their actions affect others, and the consequences of the things they do, and can be made to come around back to being "good" after having seen the outcomes of their behavior and actions.
Neither instance is foolproof or universal, but both circumstances are very much real ones.
Since a vampire remains themselves after turning, the only way a vampire could be "evil" is by being that kind of person prior to turning, or by doing so many "evil" things as a vampire that they've become disillusioned to the morality of it. Humans may see the bloodsucking and killing as "evil", but for the vampire it's really just food at the end of the day. If that vampire is going out of his or her way to cause more death than is necessary just for the sake of it, then that vampire could be considered "evil."
Case in point: Akasha from Queen of the Damned. She was a bitch in life, so she remained a bitch in undeath, because her egotism and self-righteousness controlled her every thought and action.
Alternatively, you can have a vampire who is considered "good," and remains "good" based on their actions.
Case in point here: Louis from the various Vampire Chronicles books, but particularly Interview. He spends as long a time as possible living off of animal blood because he doesn't want to harm or kill a human, and when he does it's to save the life of a terminally ill and dying child, who becomes his companion and pseudo-lover in a sense. Even after the story puts him through the ringer to hell and back and disillusions him, he doesn't go overboard and only does what is necessary to survive. He's not an indulgent vampire, of all things.
Finally, you can have vampires that skirt the line; ones that are in their hearts "good," but do and say things that might otherwise be considered "evil."
Ultimate case in point: the brat prince Lestat. Ultimately a good guy at heart, but a flamboyant one who needs to be in the spotlight somehow. He's brutal when he needs to be and is incredibly powerful (becoming more so after certain plot elements happen), but is still fairly moral. He feels sorrow for the reality of his existence and the existence of other vampires he knows/has turned, and weeps for those close to him. He makes it a point to only kill and feed from "evil" humans, who he discerns by telepathic powers sensing their memories and intentions. However, in spite of these things, he goes along with Akasha when she decides it's time to go on a gender war and start massacring all males because reasons, mostly because she's hot and one of the original two vampires and they have a really warped love for one another and all that good stuff. But after so long, that little voice in his head starts nagging, and eventually his morals lead to him trying to reason and bargain with her on her stance, even if such a betrayal causes them both pain beyond reckoning (vampires in Rice's novels feel emotions with an intensity humans can't even really fathom).
So yes, in summation, vampires can easily become "good," as vampires aren't inherently "evil" unless they already were so before being turned.