Yeah, if your kids were 16 or something I'd be fine with Akihabara, as it's not pornographic, just not the kind of stuff I'd be willing to have to talk about with a 7 year old if I could avoid it. If they were 14, they'd probably be more uncomfortable than I would be about the stuff you can find.
If you're going out of your way for Anime stuff, the ghibli museum is a must. I've only heard great things, but unfortunately my trip to Japan (and time in Tokyo specifically) coincided with one of the weeks the museum is closed. My wife and I are planning another trip in December and the ghibli museum is at the top of the list.
And you can easily enjoy a few things in Akihabara with a family, I'd just stay out of some of the smaller stores. Yodobashi Camera alone would probably be fun with kids, and things like super potato and gatcha alley are fine enough (though even some of the gatchapon at gatchapon alley are risque, though they're usually in the machines higher up). I can't speak for Tokyo Anime Center as I'm not that into anime.
Sunshine City is the name of the mall with the big pokemon center. It also has a store that sells exclusively ghibli stuff, and outside in the area there's a lot of shops. I only had about an hour there with my wife before I went to robot restaurant, which was one of the longer subway journeys I took at around 20-30 minutes (PS: Robot restaurant is in the heart of, essentially, a red light district, though honestly the signage is less revealing than magazines I would see in 7/11, which are relatively tame, though very suggestive).
Frankly unless you're seeking out risque stuff you're mostly OK, except in some smaller establishments. All the main tourist attractions that we went to were great. some other places a little less obvious than shrines, temples, and the history museums might be the miraikan museum, which is a really neat interactive science museum that also had tons of english signage--I speak no japanese and got a ton out of it (they're also running an exhibit on the history of video games at the moment that I'm interested in). I think there's some sort of gundam store in that generally area that would be great.
If I think of anything else let me know. I also get replies to this thread by email so if you think of something i'll try my best to answer.