Well, the obvious options are the big cities. London, Glasgow and Edinburgh are the most popular first choices.
Many of the chain hotels have special 'romantic weekend' rates which include a room, meal and champagne. Shop around for your best options. Somewhere with a nice view is always a bonus. River views are often lovely - especially when the city lights up around you and across the river at night.
Your other option is to find somewhere a little special. Why don't you look at renting a city apartment, or a country cottage? The UK has an abundance of holiday rentals. The Lake District and the Highlands of Scotland are breathtaking and perfect for a quiet weekend away. There are some gorgeous seafront apartments in Northern Ireland, and quaint country farms in Wales.
You really need to decide whether you want a quiet, calm weekend or one filled with a little excitement. In the cities you could take in a show, dine out and sip on cocktails in a trendy bar, whereas in the country you could curl upon the sofa, take a stroll hand in hand through the country lanes and gaze at the stars in the clear night sky.