I am also trying to plan a trip in London. We are arriving in Heathrow and have to make it to Park Lane by Hyde Park. I have looked at the Journey Planner on the official website. It looks like the best way is to take the Heathrow Express to Paddington and then hop on a bus to the Marble Arch. Does anyone know how far Park Lane is from Paddington Station? Is there a better way?
Plus I need to get from Park Lane to Gatwick airport. It looks like a should jump onto the Central line at Marble Arch Station to Victoria and then get on the Victoria express. Does anyone have any experience with this? Any help would be great! I want to be prepared when I get there. I am also trying to decide if I should just pay fares as we go, or get a travelcard. We are only going to be in London for 2 days as part of our Honeymoon.

Heathrow Express to Paddington is definitely the best option, then its about 1.5 miles to Park Lane. If you haven't go too much luggage you could even walk through Hyde Park to get there. Unless its rush hour I'd get a taxi personally.
Victoria is even closer (and again the train is definitely the best way to Gatwick), and again I'd get a taxi if you don't want to walk. Getting the tube from Marble Arch to Victoria isn't worth it as you have to change twice (or once if you start off in the wrong direction...). A 1 day travelcard is a good deal for getting around while you're there - its good for the bus and the tube.
Tube map - http://www.tfl.gov.uk/tfl/pdfdocs/colourmap.pdf

Park Lane runs the full width of Hyde Park. Which hotel are you staying at?

Makes a big difference - because if at the southern end of Park Lane you will be at Hyde Park corner and the Piccadilly tube line from LHR stops right there. No change of lines and a very easy trip. If on the other hand you are up near the Marble Arch end of Park Lane, then the Heathrow Express to Paddington and a cab (or a bus if you are on a tight budget) to the hotel would be a good choice. Since there are no inexpensive hotels on Park Lane, a short cab ride probably won't break you.

If you are at the Hyde Park Corner end of Park Lane the tube ride to Victoria isn't bad. Piccadilly line 1 stop to Green Park and Vicroria line one stop to Victoria. From Marble Arch you could also do it w/ just one change - Marble Arch 2 stops to Oxford Circus on the Central Line and the Victoria line 2 stops to Victoria. But the Oxford Circu tibbe station is really busy and not somewhere I'd want to travel w/ luggage.

A cab ride from Hyde Park Corner would not be far nor too expensive

We are staying at the Grosvenor House which is at 86-90 Park Lane which I think from looking at maps is closer to the Marble Arch. We are each only going to have one bag to carry. Do you think the walk from Paddington Station through Hyde Park would be doable on a Sunday afternoon?

Grosvenor House is a bit closer to the Marble Arch end of Park Lane. From Paddington to the hotel is a bit over a mile - maybe 1.25 miles. If the weather is nice it would be a fine walk since most would be along Bayswater Rd and the park - or you could enter the park and walk through it crossing Park Lane though a pedestrian subway near Speakers' Corner.

If the weather doesn't cooperate you can just catch a taxi at Paddington . . . .

The walk from Paddington is doable any time or day (Why would a walk be any different on a Sunday from a Monday?). It's about a mile, though the nicest way of doing it is across the grass and I've never tried wheeling a suitcase across our clayey soil (I'd imagine it would get pretty bogged down after a few showers).

You can stay on the paved surface along North Carriage Drive (which is also easier to orientate yourself along, since there's very little signposting in the park, and none to the individual Park Lane exits), but that's more a city street than a walk across the park.

You want the Grosvenor Gate exit. Go to www.multimap.com, input the Grosvenor House postcode, select the 1:10,000 scale, then scroll slightly west and slightly north to see the paths from Paddington. You might want to zoom out to get a map to print and take with you.

The easiest way from the middle of Park Lane to Victoria is to pop on a bus (lots of different numbers do that journey, and every bus stop in the street explains the numbers you want)Remember you can't buy tickets on board buses in central London.

To get from Heathrow to Marble Arch, the easiest and cheaper way will be to take one of the new First Great Western Link trains which are due to start running from Heathrow on Monday. They stop at Ealing Broadway where you can change to the Central Line with no stairs between platforms.

Flanneruk,

Since I can't buy bus tickets in central London, would it be best to buy single journey tickets online or a travelcard. I anticipate using the bus or the tube on Sunday to get to the hotel from Heathrow (and I know the Heathrow Express is excluded....) and from the Hotel to Gatwick on Tuesday. I just want to get the tickets or travelcard that will best suit my needs in London. Thanks!