A commonly cited rule is the 30% rule, but in a HCOL area and with aggressive savings goals, that's probably too high. With a $95k salary, your gross monthly income is roughly $7,917. After taxes, healthcare, and retirement contributions, you're likely looking at a net monthly income around $5,000-$5,500, perhaps even lower depending on your tax bracket and healthcare plan.
Given your desire to save 20% of your gross income ($1,583/month), I'd aim for rent in the $1,500-$1,800 range. This leaves you with $1,717 - $2,217 for everything else. Track your spending closely for a month to get a clearer picture of your non-rent expenses. You might need to compromise – either reduce your savings rate slightly, move slightly outside of downtown, or look for smaller apartments.