Giant robot stuff, huh? Give these a try:
Giant Robo: The Day the Earth Stood Still is one of the gold standards. The backstory behind it is wild: in the early '90s, someone wanted to do an animated version of a classic manga called Giant Robo. While the manga author's estate allowed this, they added the condition that certain characters from the manga couldn't be used. What the anime's director did, however, was to take basically every other character the author had made up for other series - magical girls, sharp-suited spies, martial artists from Romance of the Three Kingdoms, and one colossal nuclear-powered sentient robot - and jammed them together into a big happy dieselpunk wuxia heartfelt action extravaganza. It pushes around the concept of a world based on a colossal coverup revealed and re-revealed over seven extra-large episodes, centered around the question: Can happiness be achieved without sacrifice? Despite an initial appearance as just another kid's show, it grows well beyond that in scope. If you want to see a mecha story done as an opera, here it is, driven as it is by a symphony orchestra score. And if you're worried about fanservice or other content, this one keeps it clean. (Just, for your own sake, skip the Ginrei Specials.)
If you like Evangelion, or the first Pacific Rim movie, give Gunbuster a try. It starts as a parody of a tennis show, but then jumps straight into Ender's Game territory - an interplanetary war, time dilation played for tragedy, child soldiers sent to fight unknown enemies. It ladles on the teenage girl angst on top of some great action sequences. If nudity bothers you, this might be one to skip, or at least the blatant fanservice segment in one of the episodes - you'll know it when you see it. But if it doesn't, this one is a treat.
I know you said no Gundam, but if you haven't seen Zeta Gundam, Gundam 0080: War in the Pocket, or G Gundam, you're missing out - to me, those are the highlights of the franchise. G is so radically different from the rest of the other shows, it's worth a try, especially if you end up trying and liking Giant Robo.
I personally didn't like FLAG that much, but it's got a great concept: set in near-modern times, a war photographer in Not-Afghanistan is attached to a unit fighting insurgents with an experimental mecha-like weapons platform. The focus isn't really on the robot itself, but the relationships between the photographer, her mentor, and the unit running the robot. If you're looking for more mature, this one fits the bill.