Does skipping your draw step mean you still get priority at the start of your turn?

Your turn is divided into several phases and steps: Beginning Phase (Untap Step, Upkeep Step, Draw Step), Main Phase, Combat Phase, Second Main Phase, and Ending Phase. Skipping the draw step—whether due to a card effect or a rule like the one for a player who went first in a two-player game—removes only that one step from the sequence (CR 500.10, CR 103.7a).

Priority is not tied exclusively to the draw step. Under CR 117.3, the active player receives priority at the beginning of each step and phase in which players may receive priority. The Upkeep Step is a step where priority is granted (CR 502.6), so you absolutely receive priority there to cast instants, activate abilities, etc., even if your draw step will be skipped entirely.

The Untap Step is the one step where players do not receive priority as a rule (CR 502.3), but that is unrelated to the draw step skip. All other steps of your turn proceed normally unless some additional effect skips them too.

Concrete example: You control a Phyrexian Arena, which makes you skip your draw step. On your turn, you still untap your permanents, then receive priority during your Upkeep Step (letting you cast a Brainstorm or activate a planeswalker loyalty ability), and then the draw step is simply skipped before you proceed to your Main Phase.

In short, skipping your draw step has zero effect on your priority windows in any other step or phase of your turn (CR 500.10, CR 117.3, CR 502.6).