The aircraft carrier girl Ryujo in Kancolle actually has a fair amount of Hestia crossover fanart. Ryujo is short and wears her hair in twintails, like Hestia Some of Ryujo's dialogue reminds me of Hestia as well. Ryujo does, however, lack some of Hestia's... essential attributes.
I sold my soul to Japan Creative Staff in 2005, so I have a positive bias toward any show they produce. My personal blog is called H.C. (Heart's Content) Staff for a reason. Of course, J.C.Staff sometimes puts out shows that are so bad that even I have to admit it.
Having seen the first two episodes of Danmachi, I would say it isn't quite that bad.
I rather like how much like a video game it feels. Item drops, level grinding, and increasing monster difficulty based on the dungeon floor are all present. Hestia uses her power to literally display Bell's character sheet, complete with numeric ability scores, to show him how his power is increasing. Bell has a powerful passive ability that increases his experience gain and stat growth as long as he's in love with a girl. Hestia knows this, but chooses to hide this information from Bell, for reasons that actually make sense in the story, but may not exactly be wise.
So far, the show's biggest weakness is the large number of times it made me say, "Why don't they just do [insert course of action here]"? and "Shouldn't a city like this have someone who..."
Toward the end of the second episode, when an ape-like monster is released into the marketplace, there were a number of times when the thing I logically expected to happen based on earlier events, didn't happen.
Some of the "Why don't they..." and "Why didn't this happen..." questions get answered to my satisfaction later, but some do not. It makes certain events seem too convenient, or certain characters seem too stupid.
I still hold out hope for the show even if you don't count my pro-J.C.Staff bias, because I like the characters. Bell is a nice guy who owns his mistakes and does his best to make up for them. He starts off as a wimp who doesn't know the value of being in an adventuring party, but everything indicates he won't stay that way for long. One time Bell gets humiliated by a veteran adventurer while at a tavern, and runs away. But the next day he returns to pay for the food he ate. It's a minor detail, but things like that make me think Bell is a worthy hero, despite his relatively shallow motivation. (He wants to be a stronger fighter so the warrior-princess who saved his life will notice him.) As an aside, it is kind of annoying how so many of the girls in the show like him, but if you've seen enough anime you can deal with it.
The original title of Danmachi is "Familia Myth." I like the various gods from Greek and other ancient mythologies, and how they have been translated into anime form. Did you know that in Greek mythology, Hestia is the elder sister of Zeus, Hades, and Poseidon? I knew Greek Hestia was a patron of hearth and home, but don't know any famous myths involving her. Just like Greek Hestia, Danmachi Hestia lives in the shadow of the more famous and powerful gods. Hephaestus (who is male in Greek mythology, but not in Danmachi) behaves like you would expect the god of smiths to behave if she turned to capitalism. Apollo and Hermes haven't appeared yet, but I'm interested to see what they are like.
The show is fun, Hestia is cute and except for a few... attributes, she reminds me of my Kancolle ship-waifu, Ryujo. Unless the story goes completely off a cliff, that's good enough for me.