So, I had a bunch of ideas for you until I saw you’re in “long” sizing. That dramatically cuts down available options, especially since more and more brands are cutting their jackets on the shorter side now.
Still, your budget is definitely workable for a lot of Brooks Brothers options. I’d wait maybe until their Friends and Family sale (sometime in May, I think?) and get a staple navy blazer from them (big fan of this Social Primer one, which they don’t even sell in my size anymore) and maybe this linen sport coat. You could actually buy both right now and be under your budget.