It looks like you're going in mid-May, based on your signature. That's not the best time, but it's far from the worst time to go to hope for some walk-up dining options. You shouldn't fret.
First off, a few places never take ADRs... for instance ESPN Club (Boardwalk) and Beaches & Cream (Beach Club). Beaches & Cream could be hit or miss at any time. ESPN is obviously going to be busy on nights when big games are on, but other times, you should be alright.
Don't assume you must go to a restaurant at a park... nearby resorts may have less crowded options. So if you can't get seated at any of the restaurants in MK, you could try heading to nearby resort restaurants - Whispering Canyon at Wilderness Lodge (especially at lunch time, you shouldn't have a problem there); Trail's End at Ft. Wilderness; Kona Cafe at the Polynesian; Grand Floridian Cafe at the GF; or The Wave at the Contemporary.
At Epcot, you could head over to the Boardwalk or Beach Club for meals through the International Gateway... but several countries often have availability without long waits - try San Angel in Mexico, Nine Dragons in China, Biergarten in Germany, Marrakesh in Morroco, Chefs de France, or Rose & Crown in the UK.
At the Studios, Hollywood & Vine is highly likely to have availability. But you could take a boat to Boardwalk or Beach Club for other options. I think Captain's Grill may be a good option at the Yacht Club.
At Animal Kingdom, try Yak & Yeti or the Rainforest Cafe by the front of the park.
If you feel like exploring other resorts, you could take a bus to Old Key West and try Olivia's, to Saratoga Springs and try the Turf Club, or to Port Orleands Riverside to try Boatwright's (dinner only)... think outside the box. I found that the Garden Grove was a wonderful buffet over at the Dolphin, and when we dined there with a dinner reservation, we were among only three or four parties there total! (If you have
DDP, just be aware that's not useable here... but TiW is.)
Hope some of these thoughts help!