It's probably best to take a look at some tour sites to see where they all go.

In BKK:
for sure you will want to see The Grand Palace and Wat Po.
Take one of the long boat around the klongs off the river.
Visit Wat Arun while you are down in the Grand Palace area

For shopping....it is everywhere. There are the high end malls all right next to each other: Siam Paragon, Central World, Gaysorn, etc on Rama I Rd.
And there are the markets like JJ market on the weekends or the night bazaar at Lumpini.

You should plan a day trip from Bangkok to Ayutthaya at least for the old capital's ruins. If you are into those sorts of places you can also visit Sukhothai which was the original capital of Siam. There are also Khmer ruins at Lopburi and dotted around Isaan at places like Phimai.

With that much time it is also worth visiting Chiang Mai. It's a short flight from BKK. There is a lot to do and see up in that area and it is very different from Bangkok.

I think lots of people also go to the beach resorts like Phuket. If you like those sorts of places there are plenty of them.

Thailand is a bigger, more diverse place than most people realize. With two weeks you can scratch the surface but not much more.