Travel Card vs Oyster

Are you traveling alone? Or as a pair or more? If there are 2 or more people traveling together, then the paper travel card issued by National Rail Stations has the advantage of being valid for the 2-for-1 offers (http://www.daysoutguide.co.uk/2for1-london). You can get 1 day cards or 7 day cards. The 7 day cards require a FREE ID card, for which you must bring a passport sized (not quality) photo. You can also get an Oyster card and load Pay-As-You-Go (PAYGO) onto it and/or travel cards onto it. If you are traveling alone, I'd get an Oyster and load 10-20 GBP as PAYGO, and probably a 7 day travel card. Even if you just use PAYGO, the Oyster will calculate the LEAST expensive cost based on your use each day. Even on the days you are going on daytrips out of London, you may need to use the TUBE or buses to get to/from the rail station, etc. You can always add more PAYGO cash if needed, and the deposit you pay for the card, plus any unused PAYGO cash is refunded when you return it.

This is a frequent question and there are plenty of strings with the info if you use the "Search" (which isn't that easy to locate, so you may not have found it). That being said, I've not gotten a Travel Card, but last time I was in London (a few months ago) I finally bought an Oyster Card and MAN! So easy! So cool! So... why did I never do that before? You buy a card - there are large posters that suggest the right amount for your number of days, as well as helpful reps who will help you figure it out - and it's X number of pounds plus a 5 pound deposit, which you get back at the end OR you can just spend it down. Basically, the card automatically caps your day's charges for fares at the price of a one-day Travel Card. Where are your 3 day trips? That might make a difference...

If you are traveling solo, then I'd get an Oyster card. An Oyster card can hold both a travelcard and pay-as-you-go money at the same time. If it were me, I'd load a 7-day zone 1-2 card and about 10 GBP of pay-as-you-go money to start. You can choose the start date of your travelcard. When you travel outside of the travelcard's validity (either outside zone 2 or on other dates), it will deduct from the pay-as-you-go balance. You can add more to the pay-as-you-go balance if you need it.
I like the location of the Strand Palace hotel (on the Strand, a couple of blocks from Covent Garden), but know nothing about the hotel itself.

I forgot to mention I will be traveling Solo. Thanks for the responses, the 7 day travel card put on the Oyster sounds like the best plan for my travels.