I've eaten lunch at T-Rex twice with no reservations, we got there at 11:00am and were seated right away.
I would call the restaurant directly if you want a reservation. It is not on the dining plan so you should have no trouble getting a reservation.
Getting into other TS restaurants, may be a little more tricky.
Free dining tends to book things up pretty good, I would go online and see what you could get.
I have had good luck with walk ups:
Liberty Tree for Lunch
Grand Floridian Cafe Breakfast Lunch and Dinner
Kona for breakfast, lunch, and dinner
The Wave for dinner
Rainforest Cafe breakfast, lunch, and dinner
T-Rex early lunch
Tusker House lunch
Marakesh lunch and dinner
Nine Dragons lunch and dinner
Brown Derby lunch and dinner
Raglan Road dinner