Lived there for many years!
Areas to probably avoid would be Coldean, Moulsecoomb, Bevendean and Whitehawk but tbh, they're not exactly the Bronx. Lots of students will live around the Lewes Road area (along the 25 bus route) so if you want to avoid studenty areas avoid there.
Hove is a little less "young" but to be honest the city is so small and the buses can get you around so quick. I preferred Hove as I preferred living somewhere quieter but having the vibrancy within a short bus ride or walk. Hove IMO is nicer than Brighton, if I was to move back to the city I would choose Hove over Brighton 100%.
Property is very expensive down here, and quite a lot of the properties are old and can have damp issues where the landlords really don't care as they'll still be able to rent their flat.
Parking is an absolute nightmare in the inner city areas. The city is well known for it's parking enforcement and most of the place is residents only permits and you're likely to have to wait a few months before you can obtain a permit due to it being oversubscribed.
Brighton and Hove bin collectors also like to strike every now and then, that's never pleasant.
More information about you would be useful, if you're wanting to rent a flat, buy a house etc. etc.