Potty area for dogs?

Although I suggest dogs prefer to use grass, many dogs manage to empty when on concrete (kennels!!) in which case it can be regularly hosed down.   Concrete should be shaded however or it will get too hot to the feet.   Some people with kennels (or not?) use pea gravel although during times of less than normal stools, that could be a problem!!

in the sink or your mouth you choose

You can put in pea gravel (in white or tan) or you can grow grass (more ecological & natural.)  Dogs can't damage or kill the pea gravel (& even if swallowed) the really SMALL version - will go straight thru and you can hose it off or even use a mild Clorox solution, if needed.  

But green grass is much more natural & easy on the eye or the smaller liriope (aka monkey grass) is much tougher when peed on the grass.  (Either will be cooler in summer, to a dog's feet & can be hosed off or offer a absorbent area for rain run-off.)  However in the summer, you can ONLY install a warm season grass (which will turn TAN in winter) & it only comes in sod format.  It will be pricier to install & harder to get -going than a fall-installed cool season grass (from SEED) like fescue.

Grow some grass..  Walk the dogs on leashes until it grows.

Any loose material like mulch will also get tracked in and make a mess as well, tho it wont be quite as messy as mud.

Cement/pavement is going to be too HOT in the summer for dogs paws

I put in a patch of real grass, probably 10 x 12, and also have a carpeted area.  What do you consider an arm and a leg?  I had mine professionally installed for about $500.

Get real grass. Buy a patch of grass sod.