For us, the first scan (CT), was just precautionary as she'd been having headaches. We got the results in 20m, but it was 7cm big, so very very obvious, and they didn't have to analyse it that much.
Based on that, she had an MRI the next missing, to check there weren't any other bits
in her brain or spine, and to get a clearer picture for surgery, which happened immediately after (we knew this was their plan).
As we went straight into neurosurgery and there were complications, we were in for 7 weeks. But one of the others was only in for a week, and the average was 2ish weeks apparently.
For her monitoring scans (there's still some left), we are basically there for the day (8-12hrs), and get the results back in about a week. But as they giving detailed measurements of changes and they know what it is, there's less rush.
No one can predict sadly what will happen, and how long you'll be at the hospital. It could be hours, days, weeks, or rarely, months Regardless of what it is, they may need to operate, and this might be done almost immediately, or it may be a few days. If they operate, then recovery time varies hugely. It may be that either they don't need to operate or will do a different treatment instead, which may it may not be hospital based.
Many (hopefully most) hospitals with a children's neuro, have a Ronald McDonald House, for accommodation, cooking, laundry etc, but you'll also be able to stay on the ward, next to your baby. On the ward, they'll have a parents room where you can they microwave make, make tea and coffee etc. If you are breastfeeding, they'll feed you.
Neuro wards are scary, but bear in mind that every child is there for a different reason - I assumed they all had tumours etc, but we were actually in the minority.
I'd make sure to take a comfy sling with me, as if they operate, baby might be quite clingy for a while, and at least that way you can stretch your legs.
I'm really hoping that it turns out to be something easily fixable, and thinking of you all x