Tube/Train Pass-Best Option London

If you are not carrying steamer trunks on your journey I would concur with Michael S. Your description sounds like the Ridgemount Hotel or someplace nearby on Gower Street. If so, the walk from Russell Square would be very nice, even if it is actually further. Around UCL there isn't much traffic usually, just watch out for the occasional bicycle. Of course you could also grab a taxi. You could load some pay as you go money onto an Oyster card, 1 for each of you, and use that to get from Heathrow to London, then use it during your stay, then back to Heathrow at the end. Top it up as you go, and if you are coming back to London another time hold onto it and be set when you return; or turn it in and get any money remaining on it and your deposit back when you get back to Heathrow. Happy planning...

If your hotel is near Paddington Station the Heathrow Express/Connect will be the fastest way into the city. If your hotel is on the Piccadilly Line (a big chunk of them are), then the Tube will be faster as it will be a direct journey, and you'll only have to wait in one line for tickets. I always use the Oyster Card. You preload it with pounds, and it automatically deducts the lowest fare, depending on how many trips you make per day. http://www.tfl.gov.uk/

When will you be coming, Nicole? What days of the week? Engineering works can play havoc with the Underground on weekends and bank holidays. More money brings apparently faster trip in: The most expensive and slightly faster is the Heathrow Express. Slightly slower but considerably less expensive is Heathrow Connect. Both do not accept Oyster Cards nor do they accept TravelCards. The cheapest, and slowest, yet in some cases the over all fastest (or a dead heat) is the Piccadilly Line of the Underground. That is because once you have your fare into Central London it can take you anywhere in usually zero or one changes, all inclusive. The Heathrow Express and Connect take you to Paddington. Great if that's where you want to be but if not you then need a bus, taxi or Underground trip to complete your journey - that adds up. So, for the best advice, where will your hotel/hostel/flat/apartment be?

My hotel said... From Heathrow you can take the Piccadilly Underground Line which will take you directly to the City Centre. You can take the stop on Russell Square and from here walk the 10 minutes to the hotel or perhaps take a taxi. You can also take the stop at Leicester Square. Here you can transfer to the Northern Underground Line which will take you two stops further to Goodge Street. From here the hotel is only a 4 minute walk. There is as well the Heathrow Express train which will take you in 15/20 minutes to Paddington Station. From here you can take the Circle Line or the Hammersmith&City Line to Euston Square Station. Our hotel is then a 6 minute walk down the street.
Of course you can also take a taxi from the Airport to the city of London. Basically I am going to Euston Square...

In your case the Picadilly line is the best option. It will be a direct journey from Heathrow; no changes.

Buy Oyster cards at Heathrow and load some pay-as-you-go pounds on them to get you from Heathrow to London and back to Heathrow again. When you return to Heathrow you can get a refund on your deposit plus any unspent pounds on the cards. Go to Euston rail station and buy one-day, zone 1-2 paper travelcards with the National Rail logo on them (not sold at Tube stations). Use them to take advantage of National Rail's 2-for-1 offers in London. To see the offers and to print vouchers for the ones that interest you, go here.

Adding to my previous post. You'll need to buy one-day travelcards for each day you plan to use a 2-for-1 voucher. If you won't use an offer on a particular day, then just use your Oyster cards and don't buy travelcards for that day. No matter how many rides you take in a day, your Oyster cards will top off at no more than the cost of a one-day travelcard for the zones in which you traveled that day. Add more money to your Oyster cards as needed.

That was really helpful, Tim (and everyone). Thank you so much!

Upon our arrival in London, we bought one way tickets on the Underground and rode into the city. It took us about an hour to get from Heathrow to Aldgate East. Very inexpensive, although the Tube was crowded since we arrived during rush hour. I took the Heathrow Express for lack of any better options on my return back to Heathrow. We were on a 0800 flight back to the US, and all of the Underground stations near our hotel were closed for maintenance. So, we took a bus from Aldgate East all the way to Paddington and rode the Heathrow Express. The bus journey was entertaining to say the least, and our trip on the Heathrow Express was pretty quick. The zone 1-2 day passes should work well for you. I bought a London PopOut map that was tremendously helpful to use to get around the city and it also had a Tube map on it. You might check it out! They make them for most of the major cities. I bought mine at AAA, but I'm sure any major bookstore would have them.