I disagree with Capt. Aileron about avoiding Coventry. Coventry is an excellent city for staying in your room and getting on with some serious study!
Seriously though Max Drift, your best bet is to phone around, using the accommodation list that ATA can provide. Do this soon, or you might have problems finding a place that isn't already booked. There are quite a few places close to the airport, some within walking distance of ATA, and many of the landlords/ladies also provide evening meals and packed lunches if you want them. Advisable in my opinion, as it gives you one less thing to worry about.
By the way, congratulations on choosing an excellent ground school.