A car would be a good investment.
Whilst bigger cities do have better options for public transport, many of those options are not available at the times you will be travelling .
You will be working nights, public holidays , xmas day etc etc (maybe not xmas day as a student but certainly other public holidays) and public transport esp at 6am in the morning on those days is usually very limited.
You will be starting shifts at 7am in many places and that means being there, getting into the hospital building and correct floor and changed and on the ward ready to start at 7am, not just pulling up at the bus stop at 7am often buses/trains dont run early enough to get you places for that time esp if you are having to make several different connections.
Your placement may not even be in your city, many of our students have their placements in neighbouring towns because thats what they have been allocated and are up & walking several miles to train stations at 5 in the morning as no available buses.
You may want to enquire at your university where is the furthest place you would be sent on placement & what the bus/train timetables to that place are like , particular in the early/later hours and on public holidays.
If you are doing 12 hour shifts and potentially having to get connecting services after you finish it can be challenging later at night.
The flip side is that parking at hospitals if often challenging and very expensive ,
You may also want to check out repayment rules if you drop out, very often a high drop out rate in the first year of nursing.