As a stage 4 vampire, how can I feed without getting noticed?

Solution 1:

I haven't played vanilla Skyrim in a long time, but I'm pretty sure you can feed off bandits and so forth in the wild before entering town. You might have to kill off most of the camp, run away, wait until the bandit "resets" to his normal routine, then wait until he's asleep. Nom nom nom.

As pointed out in this answer, Dawnguard gives access to the Vampire Seduction ability so you don't have to wait until the bandit is asleep, but it's limited to level 10/20.

Edit: this page on the wiki says

Dawnguard removes this penalty and people will treat a blood-starved vampire like any other person.

I'm guessing you don't have Dawnguard or you wouldn't have this issue. Installing Dawnguard could be a solution if you want to buy it.