This is going to sound kind of mean, but basically anything with Johnny's Juniors. The dialogue for those dramas is really simplistic and the actors speak really slow (because they really can't act :/). Off the top of my head I can think of Pin to Kona, Piece, Sprout, Kamen Teacher, Shiritsu Bakaleya KouKou, Bad Boys J Risou no Musuko, Beginners, and Gokusen. Pretty much any high school romance drama will have simple dialogue. Boy's love movies also have that really slow spoken dialogue as well since they usually aren't very well acted. I'd recommend the Takumi-kun series.
Yankee dramas are pretty easy too since their vocabulary isn't that varied since they're high school delinquents. I can think of Gokusen, Tumbling, Majisuka Gakuen, Asuko March, and Rookies.
Tl;dr: Basically any high school drama, cheesy romance, boys' love, and dramas with yankees.
I have been watching without subs for quite a while now. For anything with more "complicated" vocabulary, I use Japanese subs since I can figure out a lot of word meanings based of the meaning of the kanji, and it makes it easier to look up words I don't know. Also, good reading practice. From what I learned, all you really have to learn is the basics of the language, such as sentence structures, verb conjugations, greetings and formalities and at least the core 2000 vocabulary before you can begin understanding anything. After that, everything will basically learn itself. I wouldn't worry myself with unnecessary complicated grammar; it isn't fun to learn and most of it you don't need. Learn the basic essential grammar, then pick up the rest from immersion.
At first, you will not understand anything, but don't be discouraged! The more you listen, the more you will understand. If you don't understand anything, just tell yourself "I don't understand this now, but I will in the future." Just keep listening and keep learning. Watch lots of Japanese variety without subtitles even if you don't understand anything. After a while you will find yourself understanding without knowing it. Listen to Japanese everyday without fail. And keep watching dramas, of course. If you have any other questions, just ask. :)