London is well-connected to most of south-east and south-west England with fast trains connecting from London Victoria and London Waterloo. Here are some of destinations which are just a two-hour train ride or so away from London.
Portsmouth is a harbour town where you can see HMS Victory...
Photo by Jamie Campbell
...and Spinnaker Tower, one of the most stunning 'tall structures' you can see on the planet.
Photo by Ballista
You can even go up the Spinnaker Tower to catch the view of from 'Crow's Nest' at the top. You have to pay for that though.
Southampton was where the Titanic sailed from, and you can see anchors from the Titanic and other maritime museums in town to check out. There are fortifications around town called the Southampton Park Gate. Also, there's a pub called The Red Lion that has been around since Tudor times, it has quite some character although these days it's a bit derelict.
The Stonehenge is near Salisbury! Need I say more? :) Schedule your trip properly though so that you make it within the opening hours. My suggestion would be to go towards the afternoon, walk around, and then stay for the sunset.
Photo by Ajuk
If you're a fan of street art, then Bristol is a lovely place to check out. Famous street artist Banksy (and others inspired by him) are based out of Bristol, and it's quite an experience simply walking down Bristol's streets and admiring Banksy's weird and statement-making graffiti. (If you come to like Banksy's work, I would highly recommend watching the documentary he directed titled Exit Through The Gift Shop.)
Photo by Arpingstone
Also worth seeing is the Clifton Suspension Bridge.
Brighton and Bournemouth
I'm loath to club these two together, but both Brighton and Bournemouth are beach towns where you can relax; probably not if it's snowing or raining though, then it's just miserable!
One reason why I would recommend going to Cardiff is to see the Welsh countryside, not many people do that when on short trips to England. While it's a big city and not very different as far as cities go, Cardiff has its own architecture worth admiring around and the near the city. More than that really, I think I just love the Welsh accent and how different the culture feels like. You can get some really funny pictures of signs in Welsh!
All the cities I have mentioned have direct or otherwise easy-to-access train services connected them to London, which makes it possible to visit and then return in a day. For the cheapest tickets, leave London outside of peak travel times in morning and evening to get 'super off-peak day return' tickets. Since there may not be enough to see in one place, you can do two of any of these on day - they are about an hour or so roughly away from each other by train - and then return to London from the second destination (although then you cannot use return tickets, unless you return to the first destination).