We lived in Brighton for about five months in the late 1990s, in fact we got married in Brighton, in the registry office not a bouquet's throw from the wonderful, extrovert, mock-Oriental glory of the Brighton Pavilion. Alas, being poor as registry office mice we had never made it inside, and thus I only know the lavish interiors of that amazing building from photos. Still, it's almost certainly worth visiting if you can afford the exorbitant fees being charged (it is now 10 GBP to enter the Pavilion, it was 5 all those years ago - I still remember, but a fiver then was easily as much as a tenner is today) as much for the artistic and historical interest, as for the connections to the Regency romances (from Jane Austin to Georgette Eyer).
In fact, the Pavilion would be a good introduction to the whole of Brighton and by proxy, to the Georgian and Regency periods in British history, very much iconic and exerting a powerful influence even now, and yet a very complex one, where the power of the Empire was just beginning to reach its apex and which marked flourishing of science, literature and particularly visual arts (painting and architecture), previously somewhat underdeveloped under the puritan/protestant influences. And yet the same time saw incredible poverty, rural and urban squalor of unprecedented extent, uprooting of the whole populations, and resulting crime and accompanying (harsh) punishments, all of which was only beginning to be alleviated in the Victorian era as a combined effect of actions of philanthropists, social reformers and increasingly influential socialism. Maybe the period owes its attraction precisely to this contrast between the highest sophistication of the mind and manners and the brutishness and squalor of the dark side of the era. Regardless of all this, Brighton is all about the Regency/Georgian periods, having been created as a fashionable resort by none other than Prince Regent himself, and until this day the most charming streets and districts of the city date to that period, with graceful crescents and terraces of creamy-white town-houses and delightful public squares.
The later periods embraced Brighton as a resort too - it was too close to London to be forgotten - and thus, over time, it acquired a Victorian promenade, a couple of typical English seaside piers, one of the oldest aquariums in England and later on a modern marina, a nudist beach, a left-leaning 1960s university and a reputation for being a gay capital of Britain. At times counter-cultural, at times sleazy, at times snobbishly metropolitan with soaring property prices, Brighton remains a place that is very much alive and, despite all the posturings of the locals, incomers and visitors, very real, with a surprising variety of things to see and do for all types of visitors. You might not like it, but if you are staying in London or anywhere south of the capital, the trip is cheap and quick ( frequent trains or an hour's drive in good traffic from the southern reaches of the city).
And if you never have been to an English seaside resort, this is your chance, and there is more to see there than just a crappy pebbly beach, tacky pier amusements and fish and chips on the promenade. But do go to the beach and the pier, the experience is incomplete without it.