Oh hey, this is my area of expertise..! Haha.
I used to work at a craft beer pub in Osaka. ヽ(´ー`)ノ
I'll add another post after this one detailing Osaka beer pubs... haha. This is going to be long. ><;
The craft beer scene has exploded in Japan recently.. in the past year or two I'd say. There are tons of craft pubs in Tokyo and Osaka and quite a few in Kyoto. There are also some scattered throughout the rest of the country as well. However, as tokyostyle said, the prices are.. pricey. Here in Osaka most everywhere will let you choose a size. Some are just Pint and Half Pint but others have quite a few sizes to choose from as well as tasting sets that are reasonable.
As for the big name breweries we hear most often here in Osaka, well.. there are a lot.

I'll throw them in divided by region and add notes on the noteworthy ones. They're all good, though.
北海道 Hokkaido
・ノースアイランド North Island
・鬼伝説地ビール Onidensetsu Ji-beer
岩手県 Iwate-ken
・銀河高原ビール Ginga Kogen Beer
・いわて蔵ビール Iwatekura Beer
秋田県 Akita-ken
・田沢湖ビール Tazawako Beer
茨城県 Ibaraki-ken
・常陸野ネストビール Hitachino Nest Beer (Of world-wide renown. Their white ale is nice.)
栃木県 Tochigi-ken
・プレストンエール Preston Ale
埼玉県 Saitama-ken
・COEDO(コエド) (Also world-wide famous)
千葉県 Chiba-ken
・ロコビア Loco Beer
・ハーヴェスト・ムーン Harvest Moon
東京都 Tokyo
・Tennoz Ale (T.Y. Harbor Brewery) (Some good IPAs here)
神奈川県 Kanagawa-ken
・湘南ビール Shonan Beer
・サンクトガーレン Sankt Gallen Brewery (quite famous in Japan. Some good chocolate beers as well as barley wines.)
山梨県 Yamanashi-ken
・富士桜高原麦酒 Fujizakura Kogen Mugishu (these guys make amazing weizens. srsly good stuff. we had a special line set up for their main weizen at the beer pub I worked at and set the gas pressure just right so that it was like mother's millk.)
・Outsider Brewing (these guys make amazing.. just about anything. but very small.)
新潟県 Niigata-ken
・スワンレイクビール Swanlake Beer
・エチゴビール Echigo Beer
富山県 Toyama-ken
・城端麦酒 Johana Beer (magicians and masters of the girly drinkable beers. They seriously have a beer that tastes exactly like Earl Gray tea. Oh yeah, normal beers too.)
長野県 Nagano-ken
・志賀高原ビール Shiga Kogen Beer (quite famous in these parts. make some killer strong beers like barrel aged Double IPAs and Imperial Stouts and the like. Their House IPA is also amazing.)
・ヤッホー・ブルーイング Yo-Ho Brewing (Yona Yona) (One of the biggest craft beers in Japan. You can find their stuff in some Lawsons. Never had a bad beer from here.. Yona Yona Ale is great, as is their "前略・好みなんて聞いてないぜSORRY!" series (the first of which I did a video on on Youtube. :x))
・南信州ビール Minami-shinshu Beer
・木曽路ビール Kiso Ji-beer
静岡県 Shizuoka-ken
・御殿場高原ビール Gotemba Kogen Beer
・ベアードビール Baird Beer (Run by an American guy and a Japanese guy. They have some tasty beers and I even saw some of them at a liquor store in the US when I went back to visit family last summer. One of the craft pubs here sells Baird for relatively cheap.)
愛知県 Aichi-ken
・金しゃちビール Kinshachi Beer
三重県 Mie-ken
・伊勢角屋麦酒 Isekadoya Beer (Good beers all around. Their pale ale is especially drinkable and delicious and they make a good coffee stout. They also recently teamed up with the beer pubs of Osaka to make a special Osaka beer. A belgian pale ale. Amazingly drinkable. Good stuff.)
大阪府 Osaka
・大阪國乃長ビール Osaka Kuninocho Beer
・箕面ビール Minoh Beer (Osaka's pride and joy of craft beer. They've won first place at the World Beer Awards in England countless times for their stout, imperial stout, Double IPA and Yuzu White Ale. This is also my home base of Japanese beerdom. I know just about every single person in the company from the president down to the owners and part-timers of the direct sale pubs. Haha. Good stuff!)
鳥取県 Tottori-ken
・大山Gビール Daisen ‘G’Beer (Good stuff all around. Especially their weizen line. Their head brewer is very bald. Good guy.)
福岡県 Fukuoka-ken
・門司港レトロビール Mojiko Retro Beer
宮崎県 Miyazaki-ken
・ひでじビール Hideji Beer
鹿児島県 Kagoshima-ken
・城山ブルワリー Shiroyama Brewery