Oddly, both of my favorite on-property places to eat are at DHS.
Starring Rolls
I truly enjoy being at DHS for opening, hurrying over to get FPs for TSM, and then sitting down with my family for coffee (or hot chocolate or milk) and a morning pastry at Starring Rolls. The mood is electric, watching guests entering the park, excitedly heading to their first rides, with the entire day at WDW to look forward to. Everything is clean, the utensils are stacked neatly, and the CMs greet you with a friendly 'good morning' hello. The weather is nearly always sunny and comfortable at 9 AM, making it wonderfully pleasant to sit outside at a table.
Mama Melrose's
MM provides good basic American-Italian food. The kids like pasta plus MM's handles Gluten Free very well. (Freshly cooked rolls for our special needs daughter is always a big winner.) At MM's, everyone in our family enjoys our meals. It's easy to get an ADR on short notice. They don't rush you. (In fact, service there is downright slow at times.) We always go later (about 7 PM). Because of its out-of-the-way location, the area in front of MM is nearly always empty by the time we finish; it is fun walking through the area feeling like you're the only ones there.