Code Geass was never really about the mech action, it was about the story first and foremost (though R2 was pretty stuff except for the ending). The mech action is more pronounced in the spinoff OVA, Akito the Exiled. It's all in CG, but it doesn't switch back and forth so it's more consistent. It's not very impressive action, but again, Code Geass is kind of meh with the action.
Gundam SEED is trash through and through (except for the music).
Gundam 00 has some ok action, but the writing is pretty junk for the second season (it has Code Geass syndrome, first season is great and the second isn't).
Gundam Unicorn has really good animation, even when it's CG. It has a bunch of references to older Gundam series (most take place in the same universe, some are in alternate ones) but you don't absolutely require knowledge of them to enjoy it.
Gundam Build Fighters is more of a commercial for the model kits and isn't necessarily mecha because they're not actually piloting them, but the action is well-animated and CG seems to be absent for those scenes.
Not sure how you'd handle old animation, but I do think the older Gundam series are better overall. 0083 Stardust Memory has great animation since it's an OVA with higher production values and it's short, so you might want to check that out.
Patlabor is great, it's comedy and action. It's about a police force that uses mechs. There's a 6-ep OVA and three movies, then a different continuity with a series and a second OVA series (same characters, different events). It's very 80s in terms of animation and style, but that's not a bad thing.
Macross is great, there's plenty of action in that (especially since Ichiro Itano worked on it, and you'll see plenty of the
Itano Circus). I think there's three series (I've only really watched the first one) and a number of movies.
One I'd definitely recommend to people who generally don't like mecha is Eureka Seven, there's a lot of focus on the characters and the animation/music are great. There's a sequel that I don't recommend watching, the first series by itself is enough.
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