I've been to Japan three times (planning 4th trip for next year) and while my interests are more anime related than theme parks these days I still visited Tokyo Disneyland/Sea (multiple times) and Universal Studios (once). Even if you say you're not a Disney fan (I'm not, honestly have no interest in anything they make) the parks are an absolute must. Before I visited I thought there would be nothing to excite me about the parks but honestly they are an eye-opening experience, DisneySea especially, theming is unbelievable and a lot of the rides are bucket-list worthy. As for Universal Studios it was ok, honestly I'm still pissed about being denied the ride on the Hollywood Dream roller coaster because my thighs were too chunky to get the lap bars down on the test seat (I was 95kg at the time, down to 83kg now so fingers crossed for next trip).
As for your other question regarding 'unsafe places' the only thing you have to worry about is touristy places like Shinjuku, Harajuku, Kabukicho and other areas with bars/clubs. There's a lot of dodgy establishments where they'll try and beckon you in by using English and then rip you off by overcharging for drinks or just plain rob you. It's never happened to me personally, but that's mostly because I'd only go to a place that actually appears on a Google review and not just wander into any random bar, club or restaurant.
On our first trip we stayed in a business hotel (like APA) in the financial districts of the city away from all the glitz and nightlife and touristy spaces. It made what could have been an intimidating and overwhelming first trip overseas a lot more relaxed and safe feeling. Plus the public transport (trains) are so good within Tokyo that even if you're staying away from the tourist areas it doesn't take long (or cost much) to get back into it. Also the hotels are a lot cheaper in these districts too.