For hack and slash I would definitely recommend Bayonetta. If you like the DMC/Ninja Gaiden type hack and slash, Bayonetta tops them all IMHO. But Ninja Gaiden 2 is also good, frustrating, but good. And another hack and slash that was surprisingly good was the Xmen origins: Wolverine, the movie sucked but the game was really good.
You said you didn?t want any FPS, but I don?t know how you feel about 3rd person shooters, so I will recommend a couple for you. I personally loved Dead Space. It is a very well made game with an amazing atmosphere, and a solid shooter. And Issac is not testosterone enhanced, and he is a space engineer, not a marine. Batman: AA is also very good, some of the best melee mechanics I have ever seen in a game, plus it is all the old cast from the Batman animated series, and that makes it even more awesome.
As for a good RPG on the 360, Mass Effect is the obvious answer. Oblivion and Fallout 3 are 2 more obvious answers, but if you don?t want FPS on your console, I would stick to ME. I would also highly recommend Assassin?s Creed. I liked the first one even though it is very repetitive, and the second one improved vastly on the first. I would NOT recommend Fable 2. It is not as good as the first and is the buggiest game I?ve ever seen on a console.
From the Xbox live arcade I would recommend a couple of games for you as well. Braid is awesome. Some of the best puzzles I have seen in a game, ever. ?Splosion Man is also some Nintendo old school platforming that I found fun. I would also recommend Geometry wars 2: Retro Evolved, another arcade style game. I think all of these have demos you can try.
Hope this helps.