Good clinics for emergencies and for flu shots?

My partner and I just go to Budapest for a 9-month stay as visiting scholars at Central European University.  We're from the US.  Any recommendationd for emergency clinics in case we need them?  I will be covered by Generali insurance, if necessary, but my US insurance will pay for emergency care, even if the Clinic doesn't take Hungary insurance.  We'd also like to get flu shots.  Any recommendations for either or for both?  Thanks.

Maybe this is a stupid question, but did you already try asking about available on campus or off campus health options at CEU health services?

http://www.ceu.hu/studentlife/services/medical-center

Your question is not stupid, I was. Don't know why I didn't think of checking with CEU.  I will. Thanks.

No worries. Moving to a new country can be discombobulating.

If it helps, I first came to Hungary in 1998, lived here since 2007, and I still am from time to time :unsure or :blink:.