No pink, no modern or obvious typefaces, nothing illegible, nothing cartoony.
More notes, which may help:
The place is a well-worn, well-loved pub/tavern in an old port called Port George, set in a fantasy world (magic, swords, etc). The port and the buildings in the old quarter, where The Rusty Cup is situated, is full of character. Nauticalia, wood, leaded panes, parts of ships, beams, some colourful store fronts, all manner of bric-a-brac around the dockside (nets, cargo, animals, people, upright, drunk, or otherwise, etc. I suppose it has the style of somewhere like Bowerstone in Fable 2, or the world in Woolfe: The Red Hood Diaries (itself inspired by the art of Anton Pieck).
It isn't a nasty place, or a dive. It is friendly, colourful, but sometimes rough when the occasion calls. It is at the far end of the port, in the old quarter, where the scoundrels hang out. Not exactly a wretched hive of scum and villainy, it is frequented by some crews, like the one featured in the book, who are often on the wrong side of the law. They aren't bad folk. Full of life, humour, and good company. If the folk in and around The Rusty Cup and the old quarter like you, you're well in. They protect their own. It shouldn't be hard or imposing, but well loved and worn, characterful, even warm. Humour or playfulness is okay too.
I don't have a hard and fast idea of what I am looking for, more of what I don't: nothing too cartoony, no text-only design, no stock photography hacked together. The cup should feature, but it doesn't have to be the only element (it can also be a flagon/tankard). There can be other nautical themed items, or a ship, anything like that - it can help lend it character and it is character that is key, really - especially as I would like this design to feature for print/merchandise. I don't have a preference on sign shape.
The cup doesn't *have* to be just rusty, it can be distressed, holey, encrusted, have something coming out of it (whether that is liquid or a tentacle, or something else - am open to ideas).