I stayed in a place about 7 miles from the Zoo when I was there last weekend. Its called Tara Lodge, and I loved it. Theres car parking and is about 10 minutes walk into the city centre. The staff are friendly and rooms were lovely and comfy too.
Argh I'm just after thinking... I had a double room and am unsure if they do family rooms, as I didnt need to book one. If you check out the site or email them they might do, I'm just unsure.