Where is the best spot to watch this show? Is there any spot in the restaurants at World Showcase where you could see it in air conditioning? If not what time do you need to claim your spot? Thanks

I cant remember the answer to your question specifically but...do yourself a favor and get Burnbaums guide to WDW
It answers this question and provided us with ALL the good info for each park.
The suggested Itineraries for each park are also very helpful.

I would suggest the unofficial guide to Disney it is great. I think I remember if you can get a table in England you can watch Illuminations from inside, but, the unofficial guide goes all through this particular question.

You can see Illuminations from the tables at Rose and Crown but they are outside (you cannot see as well from inside tables) I cannot think of any air conditioned places to view - some fun spots to try are the cafe in Mexico and the Japanese pavilion which has some cover.

You can see the fireworks from just about anywhere outside except for under a tree. Don't worry, you will find a place.

I wouldn't try to see them from indoors. Most of the restaurants are sealed so tight to keep in the AC that they are soundproof and you miss the good music.

You may be overplanning just a teeny bit. Try to make sure you are done eating an hour before the fireworks start so you have plenty of time to find a spot.