Million places along Kuta and Legian beach to hire boards. There's all pretty much the same. If you're not hiring a foamy and are hiring a real board then give it a once over and make sure there is no nasty damage already done to it that you don't make them aware of. Don't want to get charged for damage you haven't done.
Other than that, have a ball. Plenty of the beachboys that hire out the boards and run the little esky bars on the beach will also do surf lessons or know someone who does. It's pretty cheap but you get what you pay for. There's the forever popular Big Kahuna surf school in Kuta as well...a more professional outfit and they start you out on big foamies.
www.hugedomains.com/domain_profile.cfm?d=bigkahunasurfschool&e=comSome friendly advice: Don't get 'too' complacent in the water at Kuta. We've seen people drown and done a lot of rescues ourselves. It is a great spot to learn and you'll have 5hit loads of fun but there are some fierce rip currents so pay attention and be careful if you wind out out the back because there can be some pretty sizable waves at Kuta, especially when the tide shifts (which it does quickly) and watch out for other surfers...for your sake and there's.
As for places to stay...all depends on your style and budget to be honest. I tend to only spend a couple of nights in Kuta for a few days of hard partying then bail somewhere quiet and away from the crowds. Some people love Kuta others despise it. It all comes down to what you want out of your trip.
Pro Tip: don't use commission money changes, never act interested when making a purchase and don't feel like you're being rude when you ignore people in the streets.
