At Donington (which is within easy taxi range of East Midlands airport) only the hotel at the old paddock entrance is really within easy walking distance. Not cheap but said to be good. Very likely to be fully booked for big meetings.
Donington Park Farmhouse Hotel, Tel: 0 1332 862409 or
http://www.milford.co.uk/england/accom/h-l-3302.html
Next I would try the Three Horseshoes in Breedon on the Hill village. Fair walk (about 2.5 miles) but a taxi should not be too bad. Pub with some simple b&b rooms. Decent food but gets busy at times.
Tel: 01332 862738
Lots of others (but not, I think, closer, just Google Donington (note just three 'n's) and accommodation.
Regards
Jim