As you say, ねー is a (very) informal, rather masculine, way of replacing ない at the end of words.
Works for both verbs:
行かない → 行かねー
and い-adjectives (which are kind-of-verbs anyway, but let's not get into that debate here):
in fact it also works with other "-a" kanas. E.g:
ヤバい → ヤベー
Adding のだ/んだ as you do in your example is only warranted if you are making it a strong assertion: 行かねーんだよ！
And frankly, unless you spend your Saturday evenings loitering on the sidewalks of Sentâ-gai, you probably don't want to speak like that.
As a question, it works just the same as the ない form (sort of a loose equivalent to the "isn't it" form in English):
行かないか？ → 行かねーかー？
... is "grammatically" correct (with or without "明日"), but rare (sounds really rough/rude to me). Probably because ねー is a fairly colloquial form, which is only acceptable because it refers to yourself (and thus "俺が行かねー" is OK), but when you are asking the question form, you are using it on somebody else. If that person is standing in front of you, no matter how close you are, this could sound rather rude. Only acceptable context I can think of, would be referring to an abstract third-party:
This aside, the question form of ねー would mostly be used for rhetorical questions:
行かねーかー/行かねーかなー ("Hmnn... Should I go?")
or "semi-rhetorical" questions like:
アブねーなー？/アブねーかなー ("isn't it kinda dangerous?")