It's many years since I stayed in Brighton (but I still visit fairly often, so I can tell you that it's as vibrant as ever). However I remembered that the area around New Steine (which is definitely convenient for the seafront, shops, bars, etc) is packed with hotels. So I googled 'New Steine hotel Brighton' and the first hotel to appear was (unsurprisingly!) The New Steine Hotel. It's got good reviews on TripAdvisor (and, as stated, I can vouch for the location):
http://www.tripadviso...t_Sussex_England.html
http://www.newsteinehotel.com/
Search hint:
From the TripAdvisor link above, click on 'Hotels' in the 'Browse Nearby' panel. You'll then be presented with a map showing the location of all hotels in the area. By passing your cursor over the map, you'll be able to see the names of the hotels, together with their address, their TripAdvisor 'star rating' and a guideline price. Clicking on anything which looks tempting will take you to the relevant detailed page.
Chris