Firstly, you need to check the terms of your warranty. A good warranty will generally allow you to take it to any authorised dealer for that brand to do the work, however there have been cases where the warranty rested with the dealer where it was purchased from.
You also might find that if you take it to a dealer that you didn't buy it from may be less inclined to do the work - warranty work makes no money (you genearlly get half the workshop rates, and are paid based on a "factory time" that equates to less than half the time that it actually will take, and that's before all the paperwork that has to be done too) and ties up the workshop from making money - so make sure when you ask the dealer if they'll do it, that you tell them why you've brought it to them. Newly moved into the area is a pretty good reason, but telling them that you bought it at dealer X because they were cheaper, but you live closer to them so thought you'd get the warranty work done locally, is not going to make you any friends. You may still get the work done, but you might find it takes a little bit longer than you'd hoped it would...
I had a chap who tried that with us. He lives locally, but he was happy to travel 30km to save a couple hundred dollars when he bought his scooter. First problem and he came to see us, thinking that we'd be delighted to help him with the problems that he was having. I'll let you use your imagination as to how that one panned out.