Help with Trains (not Tube) in London

They're are tube stations at the airport, but the Picadilly line doesn't go to Paddington, so you would have to transfer once or twice. The HEX and Connect go to Paddington, but they are about £20 per adult for HEX and £10 for the Connect.

With four people traveling, I'd get a car service, they pick you up at the arrivals hall and drop you at the hotel. By the time you pay (cash) tube or train fares for four, and spend time waiting/riding, you could be at your hotel for nearly the same price.

Some to consider:
Just Airports
Simply Airports
exclusive airports
hummingbird cars
Swiss cottage cars
handicars

Of the ones listed, I have used Simply Airports.

As Emma says, please do share the location of your hotel. That way it is possible to give an accurate answer.

Yes, sorry about that. Our hotel is actually off the Hayes/Harlington rail station (1st stop from Heathrow). I talked with a Rail customer service agent (I think in India) and he said to get one day Transport cards? 25£ but not sure he understood our deliemma of hotel not being by any Tube station.
thanks

You can see all the rail and Underground lines in Greater London on this map http://www.nationalrail.co.uk/static/documents/content/LondonRailTube_map.pdf

Just to the left of your station on the map is the box which reads
"Oyster pay as you go fares are available between all stations
within the black broken line except for travel on:
• Southeastern high speed,
• Heathrow Express and
• Heathrow Connect between Hayes & Harlington and Heathrow."

The only real choice you have to get to London is the Heathrow Connect. That is the slower, stopping train between Heathrow and Paddington. You will see that Hayes & Harlington is in Zone 5. Prices are at tfl.gov.uk/tickets.

Oyster Cards and Travelcards are valid on the Underground, buses, and trains (Travelcards only in the purchased zones printed on the card or entered on the Travelcard Oyster). To be comfortable going around London from your hotel you will need zones 1-5. To go between H&H and Heathrow you will need a proper ticket.

"Our hotel is actually off the Hayes/Harlington rail station"

Unusual area to stay in, but I guess you have your reasons.

Getting from Heathrow has two options: the Heathrow Connect rail to Hayes & Harlington, or the 140 bus from Heathrow Central. You don't say which terminal you are arriving at for any additional advice.

Hayes and Harlington has 6 trains an hour to Paddington which take about 20mins. You can change to the underground at Ealing Broadway. As it is in fare zone 5 a one day travelcard will be £8.90 per day which you can buy from the station, valid on trains, underground, bus etc after 9:30 weekdays or you can use Oyster as Nigel says above.

Options for children will depend on their ages.

Jeanne also from Colorado and will be there next week with granddaughters. Staying in Covent Garden area so will take Piccadilly line from Heathrow but still not sure if for getting around and seeing sights while we are there if we are better with Oyster card or Travelcard and 2 for 1 option.

Much thanks Nigel/Marco. With kids 11 & 12 , I like the idea of just taking the 140 bus (had a very hard time finding the route but the website you gave is great) with an Oyster card and then using the Connect Train to get into Paddington. I guess we will walk from there but where is the closest place to catch one of the double decker bus tours?

Not that it matters much, but only two of the 6 services per hour to PAD from Hayes are actually operated by Heathrow Connect - the others are First Great Western ones from the likes of Oxford & Reading. Just take whatever turns up first though.

If you're arriving from Paddington and are looking for the closest HOHO tour, there's a few of them at the intersection of Marble Arch and Edgware Road. From Paddington Station, head out up the big long ramp to Praed Street. There's a bus stop in front of the old post office and from there you can catch a 7, 23, 36, or 436 and they'll all go to Marble Arch/Edgware Road.
Incidentally, the 23 is a really good subsititue for the HOHOs. It goes from Paddington, Edgware Road, Marble Arch (for Hyde Park and Speakers Corner), Oxford Street (for great shopping - Selfridges, John Lewis), Oxford Circus, Regent St (more great shopping - Apple Store with free wifi, Hamleys - toys for kids, Libertys, Whole Foods), Piccadilly Circus (advertising signs and lights, Eros, Leicester Square, Chinatown), Trafalgar Square (Nelson's Column, National Gallery, St Martins in the fields, Whitehall, Parliament, Big Ben - walk down Whitehall to see these), Charing Cross (the Embankment), Aldwych (Covent Garden), and St Pauls. Of course you're not going to get the loudspeaker tourguide, but you'll save a ton of money! If you have an Oyster, then you have your own HOHO travelcard after a few journeys.
It may be easier if you take a Bakerloo tube from Paddington to Piccadilly Circus directly. When you come out into the daylight, there's no shortage of HOHO operators competing for your money.
I just read on the Original Tour website that you can catch a connector bus from the same bus stop on Praed St that joins up to their regular tours. If you've got a ticket already, that should be included. http://www.theoriginaltour.com/tour-information/directions-to-main-start-points.htm