Do you need go to the doctor today,Peter?

少了 to；当need用于疑问句时前有助动词do，说明need是作为普通动词使用，后跟动词必须用其不定式，必须加to:
Do you need to go to the doctor, Peter?

sandwich是可数名词后面要加es。另外，蛋糕店一般不用cake shop,而是bakery。

need 后没有to , 正确： Do you need to go to the doctor today, peter
Sandwich 应该用+es 表示一类事物， 正确： In cities there are a lot of cake shopes.You can buy bread, sandwiches and so on.

Do you need to go to the doctor today,Peter?
In the cities,there are lots of cake shops.You can buy bread,sandwich and so on there.

在need的后面加上to
sandwiches