I'm happy to back up Stebby's suggestion of Dublin but, at this short notice, you can't get the really cheap fares. At present, Ryanair are offering a cheapest price of about �160 return (out Saturday, back Monday), for 2 people from Stansted, including taxes and charges. While that's still fairly cheap, it might not help much if you've got a really tight budget. (If you're interested and require suggestions for accommodation and activities, just post again)
It's not clear from your post whether you want to stay at a hotel or whether you simply want some recommendations for day trips. At the risk of stating the blindingly obvious, I've got to mention Brighton. It's great for both day trips and weekend breaks. You've got culture and heritage provided with the stunning Royal Pavilion and historic Preston Manor. There are some good entertainment venues, excellent shopping (especially around North Laine, with loads of quirky independent shops) and the best variety of restaurants that you'll find anywhere in the UK, outside of London. (The Viceroy of India, on Preston Street, is superb). Trains from Victoria take less than an hour to get there. If you're staying for the weekend, Brighton is a great base for touring, whether by train, bus or car. (If you need suggestions for places to visit from Brighton, just post again).
I've got plenty of other suggestions, but it would be useful to know whether you require a base to explore the surrounding area, or whether you'd rather stick with day trips. (For the former, Norwich comes to mind -or possibly even Ipswich. For the latter, I'm thinking of places such as Rochester and Windsor).
Post again and I'll be happy to come up with plenty of suggestions (as, I'm sure, many other ABers will also do).
Chris