I have had some really nice places to stay through the tourist information office.
Also have a look on Laterooms & Booking.com There is a filter for sorting the hotels that allow pets. But always put on your booking form how many dogs and the size. It should be stated on the site if they make an extra charge for dogs.
Did have the situation when I booked a hotel for Crufts a couple of years ago, when I got there they charged £10 per dog, which was an unexpected expense.
Kirk Yetton is a nice little village not that long a drive from the showground and a lot of exhibitors stayed there.