United Noodles grocery has bottled ginger beer, at least in their small Midtown Global Market stand. I forget the brand, but I've never seen it before - I think it started with a "P". And West Indies Soul has a stand in the same market, so you could try both the bottled and fresh version in the same trip.
Other places to try are Caribbean grocery stores in Minneapolis - there's one on E. Lake Street, close to the river, and there is (or used to be) one at 42nd and Bloomington. Does anyone know the names of these places?
I think Stewart's is probably the best commercially available ginger beer today. Old Tyme was great, but ridiculously rare and expensive. For a while, there was a brand called Cock & Bull available (in red and black packaging), but it disappeared a few years ago.
I'd agree that you should avoid Reed's.
One used to be able to buy Old Tyme Ginger Beer at Lunds and Byerlys for the outrageous sum of $7.99 for a four pack. I gladly paid the price as I'd been searching for it for years. Sadly, it's gone from the shelves again. I think I'll ask L/B why it's no longer available. As I am an astute web info librarian, usually able to ferret out the oddest of minutiae on the 'web, this one product is mystifying in the lack of results.
I don't say this lightly but Reeds is something to stay away from unless you want to feel ultra happy about fruit juicy tasting ginger ale. Yuck.
Blenheim's is available at Byerlys but again it doesn't have the sugar/kick quotient just right. And we don't have all the Blenheim's options. I'm ok with that.
Stewart's Ginger Beer is just too dang sweet. Probably good for a Dark and Stormy but not straight.
I'm trying to remember if the ginger drink on the menu at West Indies Soul is "beer" or something else.
Whatever it's called, the drink is mega-gingery and delicious.
I know that the Mississippi Market carries Reed's ginger ales - don't know if they make a "beer" version or not. Might be worth checking there.
Do you have particular brands in mind?