There isn't really anything that tastes like beer other than beer. As others have said, the non-alcoholic versions have gotten pretty good over the last few years.

I'm also quite partial to unsweetened iced tea. Just make a very strong tea and pour it over ice and chill, optionally add lemon juice to taste.

Cold brew coffee is also quite nice, but personally, I prefer that one as a sweet drink mixed with sweetened condensed milk.

Kombucha

Non alcoholic beer

Unsweet iced tea

I have been enjoying sparkling water flavored with hops. It's distinctly different from non-alcoholic beer, and much better IMO.

Unsweetened iced tea and cold brew coffee are also standards in my kitchen during summer. My significant other likes kombucha enough to make it at home sometimes, but I never liked the stuff myself.

how about NA beer? Everything you want and nothing you don't.

If the alcohol is the problem, there's a lot of non-alcoholic beers available in Australia these days.

Possibly a nitro cold brew? I don't know if you'd consider that a good pairing with a burger, though!

Maybe a switchel, if you make it yourself and don't sweeten it too much, leaving it mostly tart.

Unsweetened buttermilk, or even better, ayran?

Virgin Bloody Mary is really good.

Or just ... alcohol-free beer.

Rye kvass, Kombucha

If you are willing to make it yourself, kvass or ginger beer, those can be dry and sparkling. Water kefir or kombucha. All very, very low in alcohol, not intoxicating. Chinotto soda is something I buy for dry months too.

As someone else said, tonic water has a bitter edge that really hits the spot, I make a sweet non alcoholic cocktail called the Friend Zone, made with strawberry tepache (strawberry fruit kvass), lime, and tonic water, and I swear everyone thinks it's a boozy cocktail. Too sweet for what you are looking for here but it's certainly the tonic pulling most of the weight.

Gaspacho? At least it is cool and savory...

Personally, I like just plain seltzer water. (i.e. just carbonated water with nothing added.) Mixing it with a bit of plain (unsweetened) cranberry juice is good too if you want something more flavorful.

Chilled barley tea is another good hot weather drink. It was a summertime staple when I was in Japan.

In Japan they drink cold unsweetened tea.

Why a Bottle of Japanese Iced Tea is the Ultimate Summer Refresher

A ginger beer, tastes nothing like beer and is a real pickme up.

My go-to social drink is a club soda with a twist of lime

It is simple, cheap and has the added benefit of sort of looking like it might be a vodka club or gin and tonic.

Water kefir is a great alternative. You can buy it in organic shops or make it at home. The hardest part would be to source grains but once you get them started, as long as you take care of them they last forever.

It's tart, fizzy, refreshing, has flavors reminiscent of some wild fermentation sours, and can be flavored with almost any fruit after transfer (and probably hops too).

Sparkling water with pickle juice. Add bitters if you want different flavors.

There's lots of dry / tart option, especially if you like tonic water and that dry quinine taste. Add a dash of citrus or bitters and it's not much more trouble than a beer. There's also some intresting non alcoholic herbal 'spirits' that bring complex (and often dry / bitter) flavours, and could be used to make something nice with tonic or plain soda water.

ice tea?

Oh, yes, also cold black tea (no ice, no lemon, just nice slightly bitter taste. Also nice because the taste is not really fighting with the taste of whatever you eat

chinotto

80% Unsweetened iced tea, 20% lemonade. Play with the ratios. (the classic Arnold Palmer is 50/50 but that's too sweet for me.)

Malt beer or even better Kvass

If you want a savory drink, I recommend soup broth.

If you want to make it yourself, try Tepache

What about a kind of cocktail with at most 20% red wine filled with sparkling water?

It sounds weird, I agree, but it has few calories, is refreshing, is tasty and may remain cheap enough as you do not need a great wine for it.

Everyone is recommending just stuff that's not sweet, but you asked for savory.

Beef Fizz Search YouTube for videos of it.

Kombucha

Beef broth, mmmm savory!

I think Tapache might be a good idea to take a look at.

Unsweetened, iced, mint tea.

Cold fruit teas sound like they could be good for ya

Club soda

Not sure about availability or price in AU, but I like "hoplark" non alcoholic beer. Their IPAs are awesome.

Ginger soda. You can use a ginger bug to ferment soda. You can add flavors to make different varieties or you can just do the ginger base.

Its refreshing and good for you. Does have like up to a half percent alcohol... But nothing that will be inebriating.

I haven't seen it mentioned in here, but switchel is a favorite of mine. Water, Apple cider vinegar, some kind of sweetener (molasses is traditional), and ginger. Pretty easy to make a pitcher of during the summer. Tart, and hits the spot in the summer. You can also utilize a shrub for some NA mocktails.

Tonic and Angustura on ice, with a splash of lemon. I put a dab of sugar sometimes.