I've got some good news and some bad news.
The good news is that when the Sun starts to die and swells into a red giant we'll have great seats!
The bad news is that those seats will be inside the Sun.
If it helps, you can postpone your panic for about 7 billion years. That's when the show really starts.
I wrote about this a bit a few days ago, about what happens a star like the Sun starts to die. But to recap:
The Sun is currently a very stable star, with hydrogen in the core merrily undergoing nuclear fusion, transmogrifying itself into helium and energy. The energy leaking out of the core and into the upper layers is what keeps the Sun inflated, like a hot air balloon supporting itself. It's been doing this for over four billion years, and that's where we are now.
But, over time, helium builds up in the core. It takes a lot more pressure and higher temperature to fuse helium, so for now the helium is inert. It just sits there, slowly heating up. In roughly 6 billion years the Sun will run out of hydrogen in the core, but ...