You are in for a treat!
I will include a few pictures for you as well!
First off, the number and ease of the luggage you have will make a large difference. We always take the tube, (NOT the express to Paddington) and get out at the intersection of Hyde Park and Green Park at Park Lane.
We then walk up on the East side of Park lane a few blocks to the Grosvenor. It's that simple. If you have a lot of luggage, you may need a taxi from the tube station, but try to avoid shuttles from Heathrow as it will cost you plenty.
While at the JWG, enjoy a small but charming Concierge Lounge, the staff is great! Likewise, for a relaxing pup experience visit the Audley on Audley Street just out the back door away from the park.
Please remember to use the "Big Red Bus", as you can't get a better way to see London and it leaves across the street from the Hyde Park side of the JWG.
A couple of things:
80 pounds to take the train from the airport to downtown is way more than I have ever encountered.
Even the thought of driving in London should never be considered for anyone who is not a local. You would be better served spending your holiday in a straight jacket at your most despised in laws!
80 pounds does seem excessive doesn't it Jerry. It was awhile ago now but that was probably for the three of us in 2009. I just priced the fare from Paddington to Heathrow on http://www.heathrowexpress.com/Home for 26 pounds pp first class.
Alternatively we have purchased Zone 1-2 & Zone 1 5-day Oyster cards with a one way single day extra fee to travel from Heathrow terminal 4/5 to Zone 1 where we switch to the Tube and the price was extremely reasonable. A one way fare from Victoria to Heathrow is 5 pound cash/4.50 Oyster: http://www.tfl.gov.uk/tfl/tickets/faresandtickets/farefinder/current/default.aspx.
Honestly, driving in London isn't that big of a deal if you've driven in especially Boston or LA and even Dallas/Houston during rush hour. But I agree that I wouldn't recommend it for anyone who's not used to driving in big city bumper to bumper at high speed traffic or who is freaked out driving on the wrong ;-) side of the road. Except for a couple visits when I had an automatic transmission on other visits I've rented a manual transmission vehicle for significantly less money. If you select an auto you pay through the nose, at least with Hertz. There's other local rentals over the web I've noticed for much less but I've never used them so I can't recommend. With a manual you have to clutch/shift/AND drive on the left side of the road which I don't recommend your first attempt at driving in London as that would be dangerous.
I did return for 23 days in May 2010 on a father and son trip and while in central London (Marriott County Hall! What an amazing property!!) we just Oyster cards from Heathrow and the Tube, bus and good old feet for five days where we accumulated numerous blisters on blisters and applied lots of plasters! We rented with Hertz in London by Victoria Coach Station and drove all around the country surrounding London to many POIs. What a great trip!
The last two rentals I've rented a VW Passat TDI BlueMotion with a manual. It's an imperial gallon but I got >56MPG in this thing and drove over 1300 miles on this latest trip! That was lots of stop/go's/round abouts. On VW's web it has a rated 89MPG. Amazing! Wish I could buy one in the US. Better yet, a TDI Bluemotion Hybird would be even better with deisel (and gas) prices going up again.
It is 64 pounds return to take the Heathrow Express to and from Paddinton Station. Under 10 pounds should get you a taxi from there to your hotelg. Total cost of 84 pounds return.
If you want to take the tube, it takes a long time, you switch stations, struggle with luggage, etc.
Buy an oyster card to get around on the bus/tube/etc