I agree with almost all the suggestions made by others: cleanliness, good amenities, and so on. However, what makes the biggest difference for me is that elusive, hard-to-define thing called 'the experience'. I like clean showers and a good quality bed just as much as anyone, but if I show up and am warmly greeted by a genuinely friendly host who is clearly doing his or her best and creates a welcoming environment, that makes up for almost everything. The overall ambiance and 'feel' of the albergue is more important than any specific characteristic.
I don't do the Camino for the comforts (though I'll certainly take them when I can). While on the Camino, I'd rather sleep on a thin mattress on the floor in a shack with no electricity, but hosted by someone who knows how to create a great environment, then stay in a perfectly appointed but inhospitable assembly-line place.
If I'm in Paris on a two-week vacation with my daughter, then my priorities and interests would be different. The Camino is a different sort of journey. I'm not looking for a 'Paris' experience. And when I *do* want greater creature comforts along the Camino, or just a night away from snorers and 5am risers, that's when I'll opt to stay in a pensión or hotel for the night.
My favorite albergue memories almost never have anything to do with the specific attributes / amenities of the place, but instead with the 'little' things - the genuine welcome, an immediate sense of 'belonging' ("my home is your home"), the social ambiance, the communal dinner (even if informally arranged by a sub-set of the guests), the confidence that I am in the good hands of someone who genuinely is looking out for me, the sense that while there is nothing wrong with an albergue earning a profit their every action isn't about squeezing every last possible euro out of me (indeed, I'm perfectly happy to pay a higher price up-front than to be 'squeezed'), and so on. A building with 'character' or history is also nice, though of much lesser importance.
About the only amenity that will often be the deal-breaker is wifi - I can't 'go dark' on my family or on my company. I need to stay in touch. I can go without for one night, if necessary, but that will almost certainly make it a deal-breaker on the next night.
Good luck with your venture!