You can generally get in line shortly before midnight and they will let you ride. So if you can stay until 12:30 or 1 AM, you can try that to ride Indiana Jones or Space Mountain (or any other ride, for that matter), as long as you're in line before midnight.
I agree that most of the FPs will probably be gone by 5 PM. If there are any left for Splash Mountain, it will be only because the return times are really late--most people do not want to get soaked at 11 PM.

I would think that Buzz Lightyear may quite possibly have FPs left, though, if that interests you.
Someone will correct me if I'm wrong, but last I heard, Indiana Jones may also have the Single Rider option, which should get you through much more quickly.
I like MAH4546's list...they're not all MY must-dos, but I can see where they'd be great for someone who is familiar with WDW. PotC and Space Mountain are my biggest "must-dos," but you'll probably be facing a pretty grim wait for Space Mountain without a FP.

I love Big Thunder Mountain too, even if others say WDW's is better.
If you are into history of Disney parks, then try to make time for the Sleeping Beauty Castle walkthrough. It will only take a few minutes and it is based (for the most part) on blueprints for the original walkthrough that went in a couple years after
Disneyland opened. It's pretty neat.
Toontown is way different than WDW's so I agree that if you like that sort of thing even a little, you should definitely drop in. Roger Rabbit's CarToon Spin is worth riding. Toontown closes around 8 PM (?) for fireworks and does not re-open, but the crowds are quite small at that time as well.
The whole Adventureland/New Orleans Square/Frontierland area will be crowded/sometimes hard to navigate due to Fantasmic shows at 9 PM and 10:30 PM. Most people agree that it's a better show than WDW's, and if you had even a full day in the park I'd recommend giving it a try, but since you only have a few hours, I'd skip it. DURING the show can be a good time to ride PotC and maybe HM, but AFTER the show, both those rides will be crowded, so I would plan accordingly.
Anyway, I would keep my "must-do" list small to avoid disappointment and frustration, but devise a plan to add in the "nice to dos" if it's possible. If I plan to do too much and then don't manage to fit it all in, I find it frustrating.
Have a wonderful time!