Teuchi Soba No Taguto 手打蕎麦のたぐと
This is perhaps the most popular place for soba in the city so you might have to wait in line a while to get in if you go during peak hours. The soba noodles are handmade, and taste so fresh and delicious that even people who aren't that knowledgeable about quality in soba will definitely know that they're eating something special. The chicken broth soup that comes with it is deeply satisfying too, and the fresh veggies and mushrooms are just the perfect complement to this dish. Just dip the noodles in the soup and enjoy a great meal full of Hokkaido local ingredients.
Soba Kiri Haru No Suke 蕎麦切り 春のすけ
This is really a nice place to go for an authentic experience! The place is so quaint with its old wooden facade and its simple, at-home kind of Japanese interior. You can sit at a tatami table or western-style tables. Now about the soba noodles, as is often the case for this cuisine, they are paired here with tempura. You can have them in a soup or cold, served separately from the soup. You should try that latter way of eating them if you've never had it before. They come with a dipping sauce full of umami and other side dishes too.
At a 10-minute walk from the Sapporo Station.
Soba Kiri Ukoan そば切 雨耕庵
This is an awesome restaurant! You'll feel as if you are walking in a traditional Japanese house (which is actually what it is). So you get a very authentic, experience with the hospitality that goes with it. The noodles are really tasty too! You'll notice that they have two types of soba noodles, a dark and a pale one. The dark one has a higher buckwheat content and a stronger taste, whereas the paler one has more wheat. You can have a half-and-half order to compare. Most sets have delicious tempura veggies.
Sobaya Kemmame そば屋 けん豆
Another nice soba restaurant that you might want to try because it has a really good duck soup on the menu ("kamo seiro"). At ¥1,350, it's a little bit more expensive than the other items but very worth it.
At a 7-minute walk from Hiragishi Station.
Sobaya Kono Hana 蕎麦屋 此花
They serve this really nice soba soup with huge pieces of shiitake mushrooms here. You'll love their chewy texture and the added dashi (umami, deep taste) the mushrooms add to the soup. Also, you might want to try a dish called "sobagaki", which is basically a buckwheat mochi cake that you can eat with wasabi dip in a savoury tsuyu sauce. If you want some huge tempura, they serve that too as part of their soba sets.