Aside from breed specific issues (like a7dk mentions), I would ask:
Are they a 24HR E-vet location or what E-Vet practice to they send patients to for after hours care?
What is the prevalence of parvo, distemper and other contagious diseases in your area? What are the overall vaccination rates like? If you live in a high parvo area with low rates of vaccination among the public, you'll want to be extra extra careful. If you have low parvo etc rates and high vaccination rates, then many people will do a little more socializing after the second set of shots for example.
Recommended flea, tick and heartworm prevention for your area- some areas are seeing drug resistant fleas and such. Some breeds have problems with certain medicines, so this can also be a breed specific question.
get the schedule for her next vaccines before you leave.
Get her microchipped; the % of found dogs with microchips that get returned to their owners is far far higher than those without chips, something like over 70% compared to less than 15% (among dogs that come into a shelter or animal control type facility).
IMO-
You'll want to feel comfortable with the vet and you want a vet that has both dog skills and people skills. You shouldn't feel overly rushed unless they have an emergency come in. the facility should be clean and they should clean between dogs in the exam rooms. My vet facility sprays the floors, tables and lower walls of each exam room with a disinfectant spray between dogs. Prices should be either posted or available if you ask for them, unlike human doctors who have to deal with a variety of insurance agencies and billing systems and very rarely know how much anything will cost, a vet clinic sets their own prices and the majority of clients simply pay at the time of service the set price.
If you have concerns about finances, consider a dog insurance plan now before the dog has/may have any health problems or injuries occur and start setting aside money for emergencies and a spay in the future.
I would not ask about food, I prefer to do my own research on that since nutrition is a very small part of vet school.