In reply to Mick Ward:
Mick is right in the sense that multi pitch is more complicated than single pitch and that - importantly - a lot of the difficulties may not be immediately obvious to the beginner (ie unknown unknowns). Dropping belay devices, weather changing, needing to retreat, letting go of the ropes at a belay station and watching them swing out of reach into the overhang...
That said, assuming your course was absolutely comprehensive and you are ready to rumble, my advice would be:
+ Go to Switzerland or France (i'd recommend getting the Schweiz plaisir guide books, low grade multi pitch sport climbing in the alps with an excellent level of detail)
+ I'd dial back my grades significantly. If you climb 6a, I think that means you want to be starting multi pitch climbs in the low 5s or ideally 4s, or possibly something nearer your limit if the hardest pitch is at the start, so you know you can climb it (you don't want to get stuck halfway up)
+ I'd start on climbs you can walk off the top down a proper path (ie not abseil down)
+ Pay very close attention to the quality and frequency of the bolts. Just because it is 'sport' doesn't mean it is bolted like a sport climb, the bolts might be old or very widely spaced vs a typical sport climb. The plaisir guides give you a rating for the bolts - "gut" does not mean good, or like a typical single pitch sport climb. In my experience "gut" = new bolts but very runout to the point you could break both legs if you fell off and the cruxes are often not protected in a logical manner
+ Be prepared to cheat by pulling on quickdraws, stepping on bolts, stepping up into slings you have hung off features or bolts, etc (you need to keep up a reasonable pace on longer routes because you don't know what is still to come)
+ Get proper insurance and call the chopper if you get seriously injured (don't bother with self rescue unless you know exactly what you are doing)
+ Invest in getting a proper guidebook so you know precisely where to go, what rope to take, whether you need trad gear etc. I wouldn't venture up anything based on a topo from the internet or drawn on a napkin
+ If you have the means, a guide for the day will make things much more enjoyable and massively reduce the risk of having a bash independently later
Post edited at 12:10