Minnie's breakfast at the Plaza Inn is a good option, you can get the early seating and get into the park a bit early and be fueled up, ready to go first thing after breakfast or a later seating and do some rides before brunch!
The range of characters is often said to be better and more random at Minnie's, Goofy's reduced last year and now you are guaranteed to see Minnie, Chip, Dale, and Pluto, and Chef Goofy at the door
I assume that's who moved to Paradise Pier for the temporary character breakfast there.
Tangaroa Terrace was great, too, with a few breakfast options similar to what you'd find at the counter service places in the park.
Steakhouse 55 is also super delicious for breakfast, but obviously much less kid friendly than Goofy's! Not that kids couldn't enjoy SH55 too, but it was a little quiet in there for MY liking and I felt all loud!
Carnation Cafe on Main Street is also delicious, but I am not sure if their reservations start before park opening, I suspect not.
Tomorrowland Terrace does breakfast with a few unique items, like a filling breakfast burrito.
By then, I belive Rancho Del Zocalo will have taken over for River Belle Terrace for breakfast and will be the exclusive creator of Mickey pancakes! They were also talking about adding some Mexican inspired options, too.
There are off site restaurants on Katella and Harbor, but they seemed so far away when we stayed at the DLH! We only ventured out once...! Just check out Google Maps and Trip Advisor to get a feel for what to expect.
Enjoy your stay at the DLH, I bet you'll love it anyway! We loved the cozy beds and we even watched a wedding from our room!