Can I say: What's for breakfast?
Sure you can. We always ask our spouse/parents/friends this question. But I think I agree with FumbleFingers that it "strongly implies that the speaker assumes there's only one type of breakfast available" (well, may be not "strongly").
Now this "one" type can include eggs, bread, and a glass of milk. So, if you are in a hotel where they serve only one type of breakfast that varies by days (e.g., eggs and bread on Saturday; pumpkin pie, croissants, and fruits on Sunday; and yogurt, pancakes, and juice on Monday) you can surely ask "What's for breakfast?" - because you don't know what type it will be (even though you know there will be one).
If you are in a hotel that has a wide range of items, you can ask
(a) What breakfasts do you have? (FumbleFingers)
(b) Can I get a breakfast menu, please? (Ronald Sole)
Is it correct to say: We offer bread and milk for breakfast?
Sure, if there is just that or a very few items which the guest can remember. If there are many items, you could say
We actually have a great selection of items. Would you like a menu, [sir/madam]?
or, you can be proactive and say
We actually have a great selection of items. I will bring you a menu, [sir/madam].
For some reason, I don't prefer the use of "offer". There is nothing wrong with it grammatically or idiomatically. I would say "We have coffee" rather than "We offer coffee". Its a personal preference.