For dogs.... Kentucky-31 Tall Fescue.
Once it is established, it is virtually INDESTRUCTIBLE so long as you keep it cut high. Plus, it's readily available and cheap as peanuts. Translation: if your beasts happen to kill it (e.g. Digging holes), patching it up will be a simple and easy operation. Kentucky 31 germinates in about 7 days, which is faster than Bermuda or St. Augustine or KBG can spread to fill in the area. K-31 is a forage fescue... it can stand up to rhode of cattle marching over it, eating it to the ground... and it comes back.
Another perk of K-31 fescue is that it is less resistant to bugs and insects than Bermuda, St. Augustine, and KBG... meaning that you will not likely need to apply pesticides to the lawn where your dog rolls in, eats the grass, where its toys roll during fetch, etc. Likewise, it has nice, thick blades of grass that... if cut at 3-4 inches, will block out the sun that weeds need.
A mature stand of K-31 is very low maintenance. It literally is taking over parts of the US without watering, fertilization, etc. About 3 months after it germinates, you will have a nice lawn for your dog to romp around on.
I used K-31 for my dogs backyard kingdom when I first moved in to my home. Since then, I've overseeded and/or patched some areas with TTTF, elite TTTF, Kentucky Bluegrass and/or Perenniel Ryegrass. So far, K-31 has outperformed everything and is still about 95% of my backyard,
my front lawn is my show case lawn, and I wouldn't ever consider k-31 for that type of purpose. But my backyard is for the dog, and I don't care if it doesn't have expensive, elite cultivars.
Q