Why not hire remote?
This accurately reflects the buying power in the two different cities but base pay also generally translates percentage-wise into other benefits like 401k matching and your negotiating position for salary at your next job.
I totally get that there's lots of enterprises that just aren't set up, culturally, to work with a distributed team ... but you know what, maybe that's how you (OP) can differentiate yourself from your competitors; by hiring the best talent, regardless of where they are physically located. It works, there's tons of companies that are moving to this model and getting great work done.