If you search around here are a few recent threads discussing beginner surfing in Bali. Short answer is that it exists, but you are mostly on beach breaks that are ok rather than 'great' - Bali has fantastic waves if you are intermediate+, but for beginners you are generally hanging around Kuta Beach (although there are a few resorts that have some beginner waves).
Kuta beach is fine, a bit wild / rippy at times but will generally have waves; and there are surf schools from one end to the other (esp at the Seminyak end). But like any beach it is inconsistent and can be too big or too small or close out etc.
Otherwise you could go to Byron Bay in Australia (fly into Brisbane and drive south for 2 hours) or to Noosa (about the same but heading north); but it is the middle of winter here so its not going to be all that warm (still, water will be 20deg or so and air temp about the same). But beginner waves are probably easier to find and there are heaps of surf schools in both places. More expensive than Bali I would guess. Or, if you dont mind the cold, fly into Sydney and go to Manly/Bondi beaches or head down the NSW South Coast which is stunning and there are no crowds (but there are surf schools). Even colder however. I'm guessing Perth will also be viable, but I dont know the set up over there. There must be surf school.
Or somewhere more 'out there' - you could try Japan (google 'Eugene Teal') or Taiwan (except this time of year you will probably just get monsooned). Vietnam actually has some beginner surfing as well, but I gather the summer months are mostly a miss wave wise - but you can fly direct to Danang from HK (or you used to be able to), so you could keep this as a trip for winter.
But go to Bali and give it a go. If you want a nice independent teacher look up this guy
http://silversurfbali.com/ who speaks good english and will give you private lessons for about the same price as a 10 person surf school lesson. The other benefit is that he can take you around the island to find surf suitable to your standard, rather than just having to put up with whatever is going at Kuta. But there are some surf schools at Kuta where you can stay, surf all day, get lessons every day plus boards etc for a pretty good price.
Personally I'm not sure that 2 weeks in Kuta/Seminyak will be that interesting, surfing nothwithstanding, but for a break you can go and spend time in Ubud if no where else. Plus I'm old, so the Kuta attractions (bars, massages, nightclubs etc) are no longer my thing all that much; they might be yours. As a tip - see if you can get a 'villa' in Bali rather than a hotel; often they are just the same price as a hotel but you get a house/apartment, much more space, more privacy etc.