Don’t ask about exit ops (where you go after that job), but you can ask about how the career path goes within the company (the types of responsibilities they expect to give you if you perform well and grow with them). You might also ask about when your performance will be reviewed. Something to consider asking for is an early performance review, so that you have the opportunity for promotion based on the company’s calendar rather than the date that you were hired. Sometimes companies take off-calendar year hires and figure they can keep them at a lower title (and pay grade) for an extra year because the first year isn’t a full year and then the next year you have to wait until the calendar kicks in. But remember, these days, it’s just good to have a job and income in your field, so just be sensitive to whether your requests are getting the “oh, of course we can do that” type of response or the “gee, what else is this guy going to ask for” feeling. In any case, congratulations!