Hi Mate,
I have lived in Brighton for the past 10 years. Best areas to live in Brighton in my opinion ...
Hanover area - Very hilly, terraced houses, 20 min walk to town, lots of decent pubs and youngish families
North Laine - Trendy bohemian cafe/pub/boutique area. Probably one of the most expensive areas in central Brighton. Very lively. Young fashinable crowd.
Kemp Town - Has a kind of community, village feel, again lots of pubs, near to seafront, where the main gay area is centred around.
Lewes Road - Long road that goes from the seafront up to Falmer, so you will probably need to go this way if commuting to Falmer. Slightly run down. Tends to be a cheaper area, lots of student properties centred around here.
All of the above areas are on or near to a main bus route to Falmer (25). Parking will always be a problem in central Brighton, so Id advise use public transport. Most places (apart from Falmer! are walkable).
Preston Park area and some areas in Hove also nice, more family centred and more of a problem to get to Falmer from though ...
Hope this helps!