Hiya. You are going to have a great time at SW - try not to stress too much. You should be able to see everything in the one day - especially if you are not interested in the rides (although there are really only 2 adult rides, so you would have time for them too.)
I can't help you with Sharks Grill because I have not eaten there yet, but others have said it is good. I"m hoping to try it on my next trip to SW.
I don't know about a best day, I don't know that it matters all that much. I would think the time of year you are going the park should be fairly quiet.
For discounts I would check
AAA prices if you have a membership. Also look on the SW website. Sometimes they will offer advance purchase internet only E-Ticket deals. Since you have some time keep a lookout for specials. I've seen Pepsi offer a $10 discount before. I've also seen discounts at Wendys before. I will keep an eye out and let you know if I see anything.
My best tips:
Go to the SW website just before going and confirm the operating hours and print off a show schedule. This will give you a heads up for planning your day.
Get there early - when the park opens. They will usually let you into the parking lot 1/2 hour before opening time. Be there then, get a front row space. Have your tickets purchased beforehand and line up at the turnstiles ready to go in when they open. You will avoid a lot of crowds this way. (Same as at Disney)
My first stop is alway the Stingray Pool. They usually have the food booth open right away. Get a tray (or more) of food and enjoy feeding and petting the Stingrays. After you feed the stringrays have a look at the turtles, visit the dolphin underwater viewing area, and the manatee and alligator exhibit.The Dolphin Feeding usually opens up at 10am (when the park opens at 9am). I usually have enough time to do all of that and get to the Dolphin food booth just before they open. I suggest one person get in line and the other person get a spot by the dolphin pool. Feed & pet the dolphins. The first Dolphin show is usually about 11am. Which is usually perfect timing for after feeding the dolphins. That is almost always how I start off the day and it works great.
Get to the shows when they open the stadiums - usually 1/2 hour before the show begins. You can grab a good seat and put your feet up and relax a little. If you see that things are really quiet when you are there, you may only have to get there 15 minutes early. Be sure to get to the Sea Lion & Otter Show early. You don't want to miss the pre-show mime. It's hilarious.
I am an animal lover, so I usually concentrate on the animal shows first. Then if there is time I will take in the other shows. The other shows are good, but the animals take priority for me.
I hope all of this helps. I might be able to give you more tips later, but now DH is telling me it is time for bed. Let me know if you have any other questions and I will do my best to help.