Short visit, big city, stay in London!!! So much to see, do, explore. Sorry no seaside beaches but you might enjoy mudlarking ( Google).
Drinks are easy to find as pubs are plentiful and unlike American bars pubs are meeting places for families, friends, etc so don't be alarmed to see children, dogs, and grand mums and dads all gathered in a pub. Children will be gone by 7pm.
Good food is everywhere now in London. For example near St Paul's Cathedral ( one of the few buildings not destroyed in the Blitz) is a shopping Mecca called One New Change. Stellar free view of St Paul's and London for its rooftop and a potpourri of restaurants to dine at. Food trucks are also popular so check to see what ones are where by Googling Food Trucks London. Loads of websites to research. As London is a melting pot of cultures there are countless wonderful ethnic food options to enjoy. Interestingly enough last November I couldn't help but notice how many gourmet hamburger places there were so if you are jonzing for a cheeseburger don't fret you'll be able to have ones other than those from a Mickey D's or Burger King. Pub grub is tasty as well.
As far as historical sights I'm a bit bemused you asked, then again you are in your 20's. So if you know nothing about this incredible city's long history I suggest you first stop be the Museum of London. I also suggest a visit to Westminster Abbey, the Churchill War Rooms, The Tower of London, The Treasure Room at the British Library, and Greenwich.
A cultural experience can be had by participating in an evensong. Try going to St. Brides. Easier to get into than Westminsters or St Pauls . Other options are: Visiting Portobello Road Market. Although i suspect you'd like Brick Lane a bit more. 20 year olds were en mass there last visit. Going to theatre
( buy same day 1/2 price tickets at the booth in Leicester Square). Or merely wandering through one of London's lovely parks. Regents, Hyde Park, St. James, Kensington Gardens, Hampstead Heath and people watching. You can rent bikes to do this.
Lastly check and see whats happening at Wilton's Music Hall. And review Timeout Magazine online. Will tell you virtually all that will be happening in clubs, museums, galleries, etc.