Joe gave me three words, "Giant Robots. Adventure. Optimism." It's actually the word "Optimism" that makes this one a challenge (you can find plenty of depressing stories about giant robots but optimistic ones? Not so easy).
In the end, I went to Jason Thompson's wonderful Manga: The Complete Guide for inspiration -- although I'm familiar with each of the anime franchises these manga are based on, I should note that I have not read these titles. However, each was given at least 2.5 to 3.5 stars out of a total of four stars in Thompson's guide book which is good enough for me.
Finally, I want to thank Michelle Smith (see her helpful manga reviews here) for literally being a resource (she's practically a database of manga titles unto herself) I've been drawing on as I continue to work on these specialized manga recommendation posts. Don't blame her, though, for some of my more crack-ish choices. She's just been kind enough to come along for the ride and volunteer a number of very helpful suggestions.
1. Eureka Seven, by Jinsei Kataoka & Kazama Kondou, published by Bandai.
Description by publisher: Renton Thurston's a young 14-year-old who is tired of his monotonous life. The only thing that makes him happy is when he "lifts," an extreme form of aerial hoverboarding. His feelings of frustration come from his life of toil in his Grandfather's garage and being the son of an enigmatic yet legendary "hero." One day, a large LFO (Light Finding Operation) craft called Nirvash falls from the sky and a beautiful young girl named Eureka emerges and asks for repairs. When a smitten Renton literally falls over himself to help her, the two begin a journey that will change both of their destinies.
2. Mobile Police Patlabor, Masami Yuki, published by Viz Media (Only 2 volumes published in the U.S.).
Description by publisher: In this adventure story, the brave rookies of Patlabor Section Two begin their training. On their first mission in the field, the squad finds itself up against a terrorist Labor (a humanoid robot) rampaging in Tokyo while the media, the police, and the world watch!
3. Mobile Suit Gundam: Ecole du Ciel, by Haruhiko Mikimoto, published by Tokyopop.
Description by publisher: Ecole du Ciel where aspiring pilots train to become Top Gundam! Year is 0085 of the Universal Century. Daughter of a brilliant professor, Asuna is a below-average student at Ecole du Ciel. But with the world spiraling toward war, Asuna is headed for a crash course in danger, battle, and most of all, love... Set in the original Gundam universe, renowned artist Haruhiko Mikimoto has created the perfect series for anyone who hasn't yet been introduced to the wonderful world of mobile suits!