I’m pretty sure Halo Burger will be serving Vernor’s as long as both companies are still in business.
Green River I see here and there in the Chicago area. Not common, but I see it around. Does Big Red count? I’ve seen it in Kansas City, but it’s a regional soda, so I don’t know if it’s super common there and elsewhere (I think it’s a southern thing?). Loganberry I know from Buffalo, and I think the Ted’s outpost in Phoenix has it, too. I know they sell it, and I assume it’s on the fountain, but can’t remember.
Quite a few… trendy* fast-casual places in Dallas, Austin and Houston have the Boylan, Maine Root or Dublin Bottling cane sugar sodas instead of the almost ubiquitous Coke/Pepsi options.
*you know the type of place- ones where they’re actively trying to be cool and hip.
There’s a local burger joint chain(Twisted Root) that makes their own strange root beers on a periodic basis (weekly, I think).
I’ve seen that in a lot of Seattle restaurants too. For that matter, for a few years Seahawks Stadium/CenturyLink only sold Jones Soda. They now sell Coca-Cola.