Marriot Residence Inn in New Roc City New Rochelle 914-636-7888. I have driven there many times from the Bronx (for the movie theater). I lived pretty close to AECOM and it took me 15-20mins., but I also know the area well. It is right off the highway (New England/95). This hotel lists the Bronx Zoo as 10 miles from them, and the Bronx Zoo is probably 7mins from AECOM, so that should give you some idea of the distance.
Radisson Plaze at 1 Boston Post Rd, New Rochelle. This hotel is about 2-3 blocks from Marriot. This is even closer to the highway. 914-576-3700.
You should have no trouble getting a cab although I have no way of knowing how well the driver knows his/her way around the Bronx.
For motel in the Bronx: Oasis Motel 3801 Boston Rd.
www.oasismotelbronx.com.
Pelham Garden Motel. 1990 E. Gunhill Rd.
I really cannot comment on the reputation of the two motels. There are several others but I don't remember their names.
It will probably cost you $10 by cab from the motels, more from the hotels.
I have stayed at both the Radisson and Marriot. Marriot is a nicer location as it is upstairs from the movie theater, resturants, skating rink, bowling alley and fitness club in New Roc City, although I doubt you would be staying there for any of those reasons. I would still stay with a student though.
Hope that helps.