As the saying goes Art is in the Eye of the Beholder. Thus here's my take for a first time visitor to the vibrant city.
Use the internet to see what's on at The Royal Academy of the Arts, Somerset House, and the V and A. If you see something of interest then go.
Secondly and as a great way of introduction to London's East End sign up and take one of these fun and informative tours: http://www.freetoursbyfoot.com/london-tours/walking-tours/london-graffiti-and-street-art-tour/ OR http://www.shoreditchstreetarttours.co.uk
As far as museums to see on your first visit I always recommend the Museum of London because it does a great job of detailing how the city you are visiting evolved. There's also information on the Royals.
For a historical perspective you can't beat the Treasure Room at the British Library. On display will be a Gutenberg Bible, the Magna Carta, Handel's hand written Messiah, Beatles lyrics and the original Alice in Wonderland. I love this room and the library gift shop is great! Nice cafe as well. If you arrive by tube at Kings Cross don't miss seeing the large and I mean large statue in the adjoining St. Pancras station. If you decide to go to Paris you'll see it anyway as it's where you board the Eurostar.
The Tower of London is a must see for a variety of reasons. The history, the Crown Jewels, the Beefeaters, etc. Get there before it opens, buy your ticket and when the doors are opened head straight for the Crown Jewels. After your visit walk along the river path and snap photos of Tower Bridge. Then walk up to the glass covered Leadenhall Market Place. I find this area interesting because of the meld of old and new architecture. Especially the Lloyd's of London and 30 St Mary (what is referred to as The Gherkin which you can see from the grounds Tower of London, old and new). From here you could walk up to Spitafields' Market Place.
As far as seeing Greenwich: http://www.visitgreenwich.org.uk/how-to-get-here/
If you are into Photography you might enjoy seeing what's on at the Photographer's Gallery off Oxford Street. http://thephotographersgallery.org.uk Then you could meander around SOHO and Carnaby Street maybe even sticking you head into Liberty department store which for me was an "oh my" moment.
Obviously Parliament Square where you'll find the Houses of Parliament, Elizabeth's Tower housing Big Ben, and Westminster Abbey. Quite lovely as dusk starts to fall and everything lights up.
I find both Portobello Road and Camden Lock markets much fun. Might not be others taste but my state of mind when traveling is mingling and meandering which is easy to do at both. I especially liked strolling along the Regent's Canal from Camden Lock Market to Regent's Park. OR go the other way toward the Kentish Town Underground. This whole area has undergone a huge gentrification in the last few years. Many wonderful cafe and shops now line Kentish Town Road. I stayed in the area for a few days last November and enjoyed the coffee and pastries from the tiny The Fields Beneath cafe near the Overground Station, dinner at Wahaca above the Underground station, dinner at The Oxford Pub. great lunch at The Grafton (which when I was there in 2012 was an old boozer (a dive) and is now an updated and well run pub with good food) Also dined twice at the Queen of Sheba which serves wonderful Ethiopian food.
Have a great trip and as already advised by many re think the one day sojourn to Paris. Stay in London and enjoy London. Save Paris for another trip when you'll have more than a few hours to truly experience it.
