Not saying that you would need a doctor straight away, but it always gives me a piece of mind if I know where to find one.
Insurance system here is similar to the one we experienced in Germany. My husband and I pay for our covers, but children get theirs for free.
We go to MuDr. Adamkova
She speaks English, her office is close to us and easy to find (it’s just behind the local theatre, Divadlo) and, most importantly, she is very pleasant, helpful and nice to the girls :) We’ve already visited her for vaccination for the younger one and cough sirups for the older one.
Of course, if you need a doctor outside the working hours, you’d have to go to the Pardubice hospital on Kyjevská street. We went there once and the doctor, who saw us, spoke pretty good English as well.
You also have to remember that most of the pharmacies have, in my opinion, rather short working hours. I guess, I’m comparing now to the 24/7 schedule of pharmacies in Moscow. We like to go to a pharmacy in Afi Palace as it stays open according to the working hours of the shopping centre.