I've eaten by myself at Cafe Orleans. If you eat outside on the patio, you will, basically, feel like you're eating at any of the counter service locations with outside seating. But, the food is MUCH better.
Carnation Cafe on Main Street is ALL outside. Although, it gets crowded and usually have to wait quite awhile for a table.
Along those lines, Ralph Brennan's Jazz Kitchen in Downtown Disney has outside balcony and patio seating. And, EXCELLENT food (better than anything Disney offers up). I'd eat here alone ANY day. You can people watch over Downtown Disney to keep busy.
Also, La Brea Bakery has outside patio seating, as does the Catal Bar area (these are both in Downtown Disney).
To be honest, though, there are LOTS of good counter service options at DLR beyond burgers, hot dogs, and chicken nuggets.
French Market comes to mind, as does Riverbelle Terrace, Rancho del Zocalo, Bengal BBQ, Royal Street Veranda (for Gumbo in bread bowl), and at DCA--Cocina Cucamonga and Pacific Wharf Cafe offer "different" types of cuisines.