Vadodara has companies like L&T,Xylem water solutions,IOCL,ABB, GSFC, ONGC, IPCL now Reliance, Bombardier, General Motors,Kemrock, Alembic and Jyoti. Many other petrochemical companies like GACL and pharma cos like Sun Pharma, Alembic and Sarabhai of the city are also well known. It is also considered as good location for IT companies with coming SEZ. Also, a new biotech park is coming up in the city. Quickstart Global has set-up its operations in City as well and have provided employment to more than 800 people.
If you want to learn anything related to the arts, Baroda is a good place to be - you can learn classical dance, pottery, whatever ... fairly inexpensively and from good teachers.
There are quite a few sights worth taking a look at such as the Lakshmi Vilas Palace and the old zoo. If you're headed here plan a trip that lasts not more than three days because then you'll run out of things to do. And because of the fact that it is cosmopolitan, infrastructurally decent and well connected by rail, road and air, this is a good place to have as your 'hub' and make day trips to other places.