Blends into the city centre a bit, as if you continue along Western Road from the shopping centre, you'll end up in Hove. Quieter, boutique shopping is available along the main streets in Brighton's sister city.
Hove is a big place to cover in one guide, but, since part of the appeal of Hove is that it is a bit quieter and more relaxed, it's easy enough to cover the key areas.
If you continue along Western Road from the shopping centre, it becomes Church Road at Palmeira Square, which feels like a nice place to say Hove centre starts and Brighton stops. You'll initially pass a lot of bars, restaurants and pubs (see here for more!), but once you reach George Street going up away from the sea, you've reached the central shopping area, which comprises of the whole of George Street and the western part of Blatchington Road.
Just because Brighton is the more famous destination doesn't mean Hove is lacking for shops! along these two streets is a brilliant mix of clothes, supermarkets, charity shops, gift shops and home/DIY stores. You also get the bonus of it being that little bit quieter if you're looking for a gentler shopping experience (especially on a weekend).