I have 2 small dogs, 1 big and a small yard. We want room for a patio with a firepit as well as an area for the dogs. We are not allowed to install a sprinkler system per our HOA. Any ideas on what to do for the dogs? We have heard that artificial grass retains a nasty smell...

Grass will not survive high traffic. Perhaps fencing off an area for the dogs is an option. This would keep your outdoor living area separate and pet free when entertaining.

Artificial turf is carpet. It will retain pet odors. And, it looks cheesy in the landscape.
In pet area perhaps pea gravel for easy raking of pet messes or concrete for hosing off are options.

You don't say where you live, but concrete and gravel both get terribly hot for poor little pups feet. Big dogs too. Look around for a good ground cover. Asian Jasmine might hold up to dogs.

If you are designing an area for you dogs, I highly recommend decomposed granite...correctly applied it drains well and is much easier than gravel to pick up their messes or rake up leaves. it's also kinder on the dogs' feet

I have 2 German Shepherds and they do well with large bark and smaller (round) rock in the backyard.