If I play a Priest with sewers, do I get + $2 for trashing the card with sewers?
You do not.

The "For the rest of this turn" bit of Priest's instructions will have not happened yet by the time you trash your Sewers card. It would play out like this.


Play Priest


Get +$2
Trash a card from your hand


Sewers triggers, so you trash a card from your hand

For the rest of this turn, when you trash a card, +$2



This was confirmed by Donald X in a post here:


  You play Priest. You get +$2. You trash a card. Sewers triggers and you trash a second card. Now Priest's "this turn when you trash +$2" becomes active. It wasn't active during either card trash.