Wife and I just bought a house. We would never even think about buying anything without grass and a fence, because we have a large dog too.
That being said, our front yard is landscaped with rocks and a few plants. The backyard is all grass. The previous owner had stopped looking after the yard just before we bought the house, and both front and back were horribly overgrown by the time we took possession. It took a bit, but I think the grass in the back will be in good shape this summer.
A couple questions about your grass though. Are they female dogs? Dog urine is pretty hard on grass, and at least males have the courtesy to whiz on the fence. Also, with new turf you need to keep dogs and people off it for a while to grow strong roots. Or do you even need to completely re-sod? Can you just top dress and seed the patchy areas?