It's only seen in a fleeting shot (around 1:41 or so, with the walking cyborg-arm trenchcoat/hat guy), but the fact that The Memory Den has a neon sign suggests it's not just background art. The question then, becomes: What IS the Memory Den? Considering it's location in the skeevy part of town, and the name "Den", it would suggest it's not exactly a reputable establishment.
So what can we do in a Memory Den? The obvious answer is that we can somehow experience memories.... but our own? Others? The latter seems more likely, as a high-tech place to remember things you might have forgotten seems kind of tame. But experiencing the memories of someone ~else~ could be quite the thrill. Especially if you can, say, purchase a 'trip' through the memories of a wasteland raider, or a 200 year old survivor.
Or perhaps the Memory Den is even more sophisticated and they can implant memories in you. Make you 'remember' doing things that you never actually did, ala The Replicated Man quest in Fallout-3 (or the Total Recall book/movie). Aside from replicants on the run, I'm not sure how many people would want to replace their memories with someone else's memories... but I suppose if you had some traumatic event in your life (raider attack, etc) that you want to forget, it could be theraputic.
What if it's tied to game systems, though? Like you can 'remember' skills that you 'lost'... an easy way to boost some skill/perk/stats and in some way augment yourself? If nothing else, it might be a handy hook for modders to have non-genre mods ---- you could go to the memory den and "remember" your life as a sword-and-sorcery Dragonborn or something.