Budapest Card.

I have visited Budapest 4 times in as many years and never got the Budapest Card, so it really depends on what you think you'd like to see and do while there--will you want to take walking tours or go to the baths? A couple of my favorite museums are either being renovated or moved--Applied Arts and the Neprajzi ethnographic. That said, the museums/sites I most highly recommend would require separate admission anyway:

Terror House
Parliament (book that in advance)
Hospital in the Rock - below Castle Hill, quite fascinating

The National Gallery is included and I really enjoyed it, and they are having a special Frida Kahlo exhibit while you're there, but you'd have to pay extra for that.

The transit pass aspect of it is probably the most useful, but you can buy that separately anyway, and the 7 day pass (hetjegy) is your best bet even if just there for 4 days, 4950 forints. You can get that at a kiosk at the airport or any metro station.

I decided I wanted to take the Buda and Pest walking tours that are covered fully by the card, so the purchase made sense for me. I rather doubt that it would pay off for most tourists.

You will have to decide how many of these you are interested in and then check what the discount is worth: I would suggest that in a 48 hour period you would have a difficult doing more than one or two. http://budapestcards.com/

The 72 hour card is 12990 HUF (about $47)
A 72 hour TravelCard is 4150 (about $15)
Here's what you get with your Budapest Card:
Included for free
Free entry to Lukács Baths.
Free unlimited travel on Budapest's public transport system (BKV).
Two free guided walking tours. One in Buda and one in Pest.
Free entry to the following museums: Museum of Aquincum, Budapest History Museum, Hungarian National Gallery, Hungarian National Museum, Capa Center, Mai Manó House of Photography, Kiscelli Museum, New Budapest Gallery, Vasarely Museum, Ferenc Hopp Museum of East Asian Art, and the Nagytétény Castle Museum
Free Pocket Guide App.
Discounts (10%-50%)
Discounts to more than 70 attractions, tours and museums including St. Stephen's Basilica, Budapest Opera House, Great Synagogue, National Gallery, Museum of Aquincum, Memento Park, House of Terror, Hospital in the Rock, Danube cruises (offered by Legenda) and much more.
Discounts at Budapest's famous thermal baths including Széchenyi Baths, Gellért Baths, Rudas Baths, Veli Bej, Lukács Baths and Király Baths.
Savings at participating restaurants and pubs across Budapest including Café Dorottya, Mátyás Pince Restaurant, Molnár's Kürtőskalács Bakery and more.
How much can you save with your Budapest Card?
24-hour Budapest Card - Save over HUF 6,000*
48-hour Budapest Card - Save over HUF 10,000*
72-hour Budapest Card - Save over HUF 15,000*

*The savings are based on one adult visiting 3 top Budapest Card attractions per day plus one thermal bath. Free public transport is also included. Visit more than 3 attractions per day and you could save even more.

How does the Budapest Card work?
1. Purchase your Budapest Card in Budapest at the airport or at one of the downtown Budapestinfo Point kiosks (Deák Ferenc tér - Sütő utca 2, or Heroes' Square - Olof Palme Sétány 5).
2. Validate your card by signing it and adding the date and time from when you wish to use your card.
3. Simply show your Budapest Card at the participating vendor and either get in for free or get a discount.

Where can I use my Budapest Card?
Attractions and applicable discounts:
Budapest Zoo 25%
Budapest Opera 15%
Great Synagogue 10%
Fishermen's Bastion 10%
Pál-völgyi Cave 50%
Szemlő-hegyi Cave 50%
The Water Tower on Margaret Island 20%
Tropicarium 30%

Museums & galleries and applicable discounts:
Budapest History Museum 100%
Ernst Museum 20%
Holocaust Memorial Center 50%
Hospital in the Rock Museum 30%
House of Terror Museum 20%
Hungarian National Gallery 100%
Hungarian National Museum 100%
Jewish Museum 10%
Kiscelli Museum 100%
Kunsthalle 20%
Memento Park 20%
Museum of Applied Arts 20%
Museum of Aquincum 100%
Museum of Ethnography 20%
Museum of Fine Arts 100%
Museum of Transport 20%

Baths & pools and applicable discounts:
Dagály Baths 20%
Gellért Baths 20%
Király Baths 20%
Lukács Baths 100%
Palatinus 20%
Római Outdoor Pool 20%
Rudas Baths 20%
Széchenyi Baths 10%
Veli Bej Baths 30%

Cafés & restaurants and applicable discounts:
Café Dorottya 30%
Fishermen's Bastion Restaurant 20%
Gellért Café & Restaurant & Pub 30%
Kispipa Restaurant 30%
Mátyás Pince Restaurant 20%
Molnár’s Kürtőskalács Bakery 20%
Restaurant Astoria 30%

Entertainment & nightlife and applicable discounts:
Budapest Summer Festival 20%
St. Stephen's Basilica - Organ Concerts 10%

Activities and applicable discounts:
Absolute Walking Tour 10-30%
Big Bus Hop-on Hop-off Tour 30%
Budapest Opera Tour 20%
City Park Ice Rink 10%
City Segway Tours 30%
City Tour Hop-on Hop-off 20%
Children's Railway 50%
Legenda Cruises 20%
Riverride 10%
Yellow Zebra Bike Rental 30%

Other participating vendors and applicable discounts:
Airport shuttle 10%

You'll note that when the card just offers a discount, it's usually a fairly small one. Also, at any given time a few of the free sights may actually be closed--museums being renovated, art galleries setting up for a new exhibition, etc.