What I would do is see what parks you're going to be in each day, and consider having one table service meal either at the park or at the end of the day in Downtown Disney or a hotel. EPCOT has the largest array of table service restaurants, while Animal Kingdom has the fewest. Pretty much every moderate and deluxe resort have at least one table service restaurant, while all of the value resorts just have simple cafeterias.
There are hundreds of options, so even if some may be booked already, there are probably many choices during your stay. However, you might want to keep an open mind because many of the most popular restaurants may already be booked solid or may only have reservations during inopportune times. Remember that you now need to place a deposit for you table service reservations that is refundable if you cancel prior to your dining time, and some restuarant experiences require full payment at the time of reservation (Ohana, Hoop-de-roo, Flying Fish Chef's Counter, etc...).
I just got back from a WDW and we used the app often for dining. You can scroll through and find available restaurants on the fly. Have the app locate you via GPS and find out what is available in your surrounding area complete with wonderful maps so you know how to get there.
Walt Disney World's Magic Kingdom
Disney's Animal Kingdom
Disney's Hollywood Studios
Disney California Adventure
Universal's Islands of Adventure
Universal Studios Florida
Universal Studios Hollywood