Something tells me I'm into something good.
In this case, does to be into something mean to be in for something?
You've been answered adequately by the others. But since your title is descriptive of a common idiom, I'll give its other more common meaning.
To be into something means to be interested in it.
"I'm into gardening, motorcycling .."
"He's really not that into you" - He's not that/so interested in you.
As you've probably guessed, the meaning in your example is a little different.