100% of Budapest is safe, so you don't need to worry.
Of course there are differences between the areas, and the district III is relatively large, so it would be helpful for us to know the streetname, then we could give you further information about the advantages or disadvantages of the area.
My home and my work place is really near to Amphitheatrum.
The area is very safe and quite upscale.
Thank you so much for replying!
I live next to the amphitheatre. It’s kind of the perfect mix of a chill neighbourhood but still relatively close to the center (~15min), plus loads of restaurants nearby.
At night is safe to walk and stuff?
Cheers and thank you guys!
In the neighborhood you can find some solid restaurants: Kéhli for traditional Hungarian (but Vidocq is alright as well, and you'll live next to it), Dang Muoi at Bécsi út for Vietnamese and a little further south Pata Negra Buda for tapas.
I'm so glad to hear that is a nice place to live.
Thank you all for all comments :)