I've been to Budapest three times in the past few years, one of my favorite cities to visit. I've never purchased the Budapest Card - I was just not very interested in the sights it has to offer. I have however purchased a transit pass which I used heavily (the 5/30 BKK Travelcard worked well for me). Note that if you happen to be an EU citizen and are 65 or over (dual citizen, perhaps?), you travel free on Hungarian public transport.
My top recommendation for Budapest is the Hungarian Parliament tour, which you can/should book ahead online. Other favorites are St. Stephen's Basilica, the Great Synagogue, Fisherman's Bastion, Castle Hill, Gellert Hill, Heroes Square, Great Market Hall, and Margaret Island (with its musical fountain). Also, if you have a transit pass, it includes the boats which go up and down the river, which is a pleasant ride on a nice day.
My favorite Budapest restaurant is Hungarikum Bisztro near the Parliament (book online at least a week or two in advance). Other faves are Cafe Kor, Borsso Bistro, and Barack & Szilva Restaurant.
I hope you have a wonderful time in this beautiful city!