I would say with some things it is ok to have them done some place where it will cost less. Crowns, bridges, root canals, all can be done somewhere else with little problem as long as they are done correctly. Something to consider when dealing in locally is reputation. Not only is it easier to check on someone's reputation, but if you have trouble later, they are more likely to work hard to keep you happy because they want to maintain a good reputation.
With Invisalign you will need to show up to the dentist office at 6 week intervals anywhere from 5-10 times. So I wouldn't recommend that unless you will be there on vacation almost every month. Also you may need something done in between those appointments so it could be very difficult to do. If you want veneers, I have had people travel from great distances to get them done. Wouldn't recommend that with braces.