Sorry, you're out of luck for the immediate area. I don't live there anymore but stayed at the Le Refuge Inn on City Island [(718)-885-2478] when I interviewed for a job about 2 years ago. Its pretty close to Einstein, and is technically a part of the Bronx. Its the ONLY close hotel to the school besides a cruddy motel by the Bronx Zoo.
http://www.lanierbb.com/inns/bb25104.html
Its a nice bed and breakfast, shared bathrooms. Price $75-190, and about $15 cab fare to Einstein. Its about a 10 minute drive. City Island is very safe and has a lot of nice seafood restaurants for after your interview.
On Manhattan I found that the hotel Belleclaire was the best deal, fairly cheap for Manhattan (<$200). Cab fare to Einstein will run about $40, or you can take the subway ($2) but you could get lost this way.
http://the-belleclaire-hotel.visit-new-york-city.com/
Just be aware that staying at either of these places won't give you an accurate feel for where you'll be living so be sure to ask some people what its like at your interview.
Or just stay at one of the hotels at the airport, there is always vacancy there and they're a better price (edit) vs Manhattan.
You don't have to worry about safety at any of these places.
