each district has a clinic to go get the vaccinations. One of the gaoxin clinics is on Zhangba road. They will give you a vaccination booklet and you pay as you go.
for vaccinations, I went several times to Tian You Hospital (in Keji Lu) and it was OK, although they don't speak english, so it's was not very easy. Sometimes, I waited a lot there (2 hours).
I also went several times to Li Ren Hospital (international hospital with english speaking doctor), also in Keji Lu. It was much more expensive, but much easier. Usually, I wrote to Doctor Tian before going there: email@example.com