My husband and I will be in london in september for 24hrs and will be staying in Paddington. I will be flying in sept 13th, 2pm and flying out sept 14th, 5pm (heathrow airport). Please recommend the places I can visit without being rushed and enjoy the city.
Well that's the weekend so you shouldn't feel rushed. You could always take a hop on/hop off bus tour of the city or a river cruise. Or take a London walk. Just depends on what appeals to you.
I was in London May 31/June 1 before going to Bath and though I had more time than you will I found Rick's book on London useful for sites that are "open late" (your Saturday evening) and "open early" (your Sunday morning). Depending on your choice of ground transportation you will get into London in no longer than an hour. Double-check, but I think the trains from Heathrow go to Paddington. Anyway, you will have from about 3:30 on to enjoy. On my Sunday I went to the Churchill War Rooms and Churchill museum, because it opened about 9:30 (double-check) and I walked right in. HIGHLY recommended and fits with your time frame. I had to catch an afternoon train from Paddington to Bath and I ran out of time in the museum it was so fascinating and complete. Anyway, if you have RIck's book, check on other sites that fit with your time frame. The other advice you got on a "London Walks" tour is good.
Most other museums are open daily from 10:00. Westminster Abbey and St. Paul's Cathedral only allow regular attendance, not sightseeing, on Sundays, and are not open late on Saturdays, either. A walking/photo safari would be nice on a Sunday morning; see Rick's downloadable Audio Tours. Speakers' Corner at Hyde Park is busier after noon on Sundays.
Allow an hour to get off the plane, through passport control, and on your way into the city. Might easily take half that. But, it might not,
Taxis, buses and the Tube to Piccadilly will take about an hour. The Heathrow Express train will take about 10 minutes into Paddington Station.
So, if it was me, I'd plan for dinner and something else on the evening of the 13th. A show?
Heathrow's international departure can be very crowded. Showing up three hours early is the usual official advice. Not always necessary, but I wouldn't cut it below 2 hours. Heathrow is busy and stuff happens.
Trade money for time; Take the Heathrow Express in to Paddington and back out to Heathrow. It will be a few dollars well spent.
How you spend your limited time depends on your interests. A Tube trip to Westminster Station puts you at Parliament, Westminster Abbey, the foot of Whitehall, very near St James Park, and just across the bridge from a stroll along the South Bank of the Thames. A walk north through Whitehall puts you at Trafalgar Square and the National Gallery.
If you decide to use Heathrow express, and it's both you and your husband going round-trip, check their website under discounts and see if they still have the duo saver fare. You have to buy ahead, but it may lop off a few $/£.
Have you been here before? Any particular interests? Will you be tired and want an early night, or are you up for late night partying? Do you like museums, history, theatre, restaurants? Up for a walk? Ride on a boat?
On Sunday you'll probably want to be moving towards Heathrow by about 1 to 1:30 so you can not be stressed trying to catch your flight. Will you have bags? Leaving them at the hotel to collect on your way out? You'll want to allow for an hour or so to finish what you're doing Sunday morning so you can get your bits and go.