Afspraak is roughly equivalent to German Verabredung. It can mean anything from "agreement"/"arrangement" to "appointment" to (in its diminutive form, afspraakje) "date". I'd say it's somewhere between "appointment" and "date" here. So fj is right: the right translation would be something like, "Get together with the King some time". Eens is indeed used to soften the imperative.

If I may be really pedantic for a moment, describing a pub as gemoedelijk is a very Flemish/German thing to do. Of course, the Flemish ring is appropriate here, given the fact that you were drinking Belgian beer, but you wouldn't hear anyone describe a pub as gemoedelijk in Holland. You can say that the *atmosphere* in the pub is gemoedelijk (although a Dutchman would probably opt for gezellig there), but you'd never say een gemoedelijk café or een gemoedelijke kroeg. Gezellig would be more like it here.