Yesterday I drove to Cambrige , is that correct?

The word "drive" is "sürmek", so literally  "Dün Cambridge´e sürdüm" is correct. However, "sürmek" is only used with a vehicle (e.g. arabayý sürdüm).

for "to drive to somewhere", you can better use "araba ile gitmek"

So I would say:

"Dün arabayla Cambridge´e gittim"

In addition, it is no "Cambridge´ye" but "Cambridge´e" because you add the suffix according to pronounciation and the last "e" in cambridge is not pronounced so there is no need for "y" in between.