Washington Heights is not that dodgy (neighborhood by neighborhood) - the problem is that it could be a 30 minute subway ride to midtown add another 10-15 to downtown.
For less than peak rents, consider the cities along the western shore of the Hudson River. Hoboken, Jersey City can be a 15 minute ride to midtown.
"the problem is that it could be a 30 minute subway ride to midtown add another 10-15 to downtown"
This is actually quite a reasonable commute, by NYC standards.
It's not uncommon to have a 1 hour commute each way.
I myself used to commute in to the City 2 hours each way. That's 4 hours of my life pretty much wasted every weekday.
In comparison, commuting from Washington Heights would have been a blessing.
One of the nicest commutes I had was from Brooklyn Heights, which was just a 4 minute subway ride from Wall St. Very nice neighborhood too. I would highly recommend it, if you can afford the rent.
For less than peak rents, consider the cities along the western shore of the Hudson River. Hoboken, Jersey City can be a 15 minute ride to midtown.