I spray the weeds with Round Up.
A sand bed is a great base for landscape blocks.
Correct. You can also periodically douse the cracks with boiling water, but nothing will totally prevent weed growth. Weeds are just the name we give to pioneer and other exceptionally hardy plant species that evolved to take advantage of precisely these sorts of inhospitable conditions.
I have nothing against the use of glyphosate in general but I would try to avoid frequently spraying any herbicide or pesticide, including Roundup, on surfaces where people and/or pets are often going to be hanging out, consuming food, etc.
The OP’s best strategy IMHO is to set out patio chairs that are low enough that the people sitting in them can just tweak out little sproutlings from the cracks and throw them into the firepit. You’d be surprised at how easy it is to keep a small paved area weed-free if you just get into the habit of plucking out the inevitable few bits of new growth at regular intervals.
Huh? I just re-read your OP twice, I don’t see anything saying you’re only interested in non-herbicidal solutions. And if you’re going to shut down discussion of glyphosate don’t post like you actually have any incontrovertible facts about it–the science on it is not at all so cut and dry and there’s lots of evidence that it isn’t a particularly dangerous chemical (in fact significantly safer than many household chemicals that don’t cause drama online.) If you had made it clear in OP that you weren’t interested in herbicide fair play, but you absolutely did not. Nothing you described in OP is out of bounds with how I manage a similar paver patio in my backyard, and I do use glyphosate on my property (I don’t use it on the patio.)
It would be interesting to mix some Preen in with the sand…
Preen?
GroundClear works pretty good. It wipes out living weeds, and includes a residual agent that prevents new weeds from taking root for a long time. They claim one year, but I suppose that depends on how thick you spray it.
Is it an impermissible comment on moderation if I observe that this “splitting off” created a confusing thread for me?
Preen is a pre-emergent, useful if spread on mulch in beds. We also use Roundup directed at the weeds. When my kid worked for the Public Works, his favorite job was using a flamethrower to get the weeds in brick surfaces.
Is really damned safe. My father, a chemist, who was quite conservative about using household pesticides and poisons, had nothing bad to say about it.
Pre-emergents are quite useful if you have the discipline to use them at regular intervals. But there’s always breakthrough weeds.
I use Roundup when I need to and it works quite well. Wait for a calm day so it doesn’t blow in the wind. But a commercial for the Roundup lawsuit showed a guy with a freaking backpack sprayer with a nozzle like a rake wading into a field spraying everything in sight. Who the hell would do that?
A photo on this site is similar:
I only use Roundup a couple times a year. Wear a mask, gloves and wait for calm days.
The spray nozzle applies it to a specific spot.
I wouldn’t want to use Round Up every day like landscapers.
I’m not concerned about my limited use.
Some (all?) of the the photos used on anti-glyphosate/anti-GMO websites have dubious relevance to actual landscaping or agricultural practices. I recall one showing workers in masks and full body suits spraying clouds of stuff on some plants that didn’t look like Roundup-Ready crops.
The aim is apparently to scare readers, as with stock photos of gloved hands holding a syringe with blue fluid about to be injected into an apple for genetic modification purposes. 
I have never used glyphosate for routine weed control, just for spot treatment, as with a persistent poison ivy plant growing out of a garage wall crack, which has survived and regrown despite concentrated vinegar dousing. I see glyphosate risk as very low, but have a prejudice against using herbicides around the home and garden unless absolutely necessary.
Beaides, it’s more fun to take out weeds with a cheap propane torch - you can almost hear them scream as they shrivel and blacken. 
I am surprised no one mentioned salt, I use it in areas like that with good success
Salt definitely can kill weeds, but if you end up with concentrated or insufficiently diluted pockets of it, it can mess with your soil fertility in ways that boiling water or vinegar applications generally won’t. There’s a reason that ancient legends spoke of sowing enemy lands with salt to render them uninhabitable.
I’m on 15 acres. I use glyphosate with my 33 gallon sprayer w/ 12 V pump that I pull behind my tractor. Works great. It’s a lot easier than clearing brush with a chainsaw.
The price of glyphosate has skyrocketed this year, though. 
Preen contains corn gluten, so if you’re trying to eliminate gluten…
Don’t eat Preen!!!
I’ve literally dumped rock salt directly on my lawn and while it killed the soil for a while, it was not at all permanent (much to my dismay).
I used to salt the center strip on my gravel driveway. I hoped it would build up and provide permanent protection but it never did. And I used bags of it.
Round up and similar herbicides should not be allowed for personal use. They have damaged the environment, and are the main cause of sick monoculture lawns, that require more water, more fertilizer, and constant spraying of herbicides.
There is literally no reason for herbicides on a personal use level.
There are plenty of reasons. There are just no reasons that you consider good enough to overcome what you consider to be the drawbacks. There is a difference between those two scenarios and clarity of thinking is a prerequisite to good decision-making.
You may well be right about the tradeoff. I may well agree with your assessment. But it’s important to understand and acknowledge that there is a tradeoff.