Is Vaseline good for your new tattoo?

No it is not good.

It is not the best thing in the world that you could be using for your new art, but it is just as good as any other product at the end of the day. Most artists will advise you to use A&D Ointment, which is used primarily on babies for the treatment of diaper rash. I've even heard of some artists who recommend using Preparation H, but I find this a little laughable. The easiest and best product for you to find and use would be A&D. You can get it practically anywhere, and it has a nice smell to it as well.