If you have a 2.7L engine like I do, there's a forum topic that has some DIY instructions that worked very well. My brother in law, who has never worked on a hyundai but has had plenty of experience with cars, changed mine in an hour. Depending on your experience, it may take a little longer, especially when it comes to getting the serpentine belt back on.
I originally found this when doing a Google search before I joined the forum. Now I have found it by doing a search on the forum itself. Use the plus (+) before the word to ensure the post has only that word. Search for: +alternator +replacement +santa
The post is entitled: 1st Gen (sm) Santa Fe 2.7l Alternator Replacement, Dimming Dash Lights, Parking Brake Light, Battery Light, Radio Changing Modes., A DIY of sorts for the SM (1st Gen) Santa Fe
My symptoms matched this exactly, so it worked very well. The key to being easy is going through the removable panel in the right front wheel well, so it involves jacking up the car on the right front side and removing the tire.
Hope this helps.