I hope you have a good time. The great thing about DLR is that it has pleasant weather virtually all year to sit outside, so there are a lot of outdoor spaces to sit and relax. Here are a few of my favorites.
Disneyland:
Hungry Bear Restaurant: It's all the way in the back of the park next to Splash and Pooh. A shaded place to eat or relax overlooking the Rivers of America
Jolly Holiday Bakery: located in the hub you get a great view of the castle and a great place to people watch.
French Market: If you want to eat at a sit down, Cafe Orleans provides good food and great atmosphere, but if you want just want to chill, next door is the French Market in New Orleans Square. Overlooking the Rivers of America and live music plays during the day. New Orleans Square in general is a great place to wander around however right now there is a lot of construction that has ruined it for the time being.
The Disneyland Railroad: better than the WDW version and includes the Grand Canyon Diorama
Disney Gallery and Lincoln: located in Town Square the Disney Gallery has rotating exhibits and next door is the Great Moments with Mr. Lincoln attraction.
DCA:
Buena Vista St: Great place to people watch, especially in Carthay Circle. There is a nice lounge inside the Carthay Circle restaurant as well. the Entertainment plays throughout the day and there is the Red Car Trolley (pictured below) if you want a relaxing ride.
Paradise Pier: During the day the area reserved for World of Color is open to take in the scenery or if you want a drink the Cove Bar is just off to the left of this picture.
Grizzly Trail: A hidden gem is Grizzly trail which is a small winding path around the main path through Grizzly Peak. I think that is the technical name for it. Anyway's it starts at the World of Color fastpass location and winds around and connects back to the main path near the back of Little Mermaid
Flo's: Any place in Cars Land is great,especially at night, but the outdoor seating at Flo's is my favorite.
And finally while not in the parks an absolute must is Trader Sams at the Disneyland Hotel. Simply the coolest bar on earth.