Drove through it to get to Hampi. It's much, much less wealthy than Goa, highly agricultural and much more the "real" India, good and bad. Roads are not great (we went shortly after the monsoon and some had been virtually washed away) and towns and villages very busy and scruffy (so what's new!).
To be honest, there's no great attraction in what we saw, which admittedly was limited, but Hampi was fantastic.

how long did it take to get there to karnataka?

whoa..you are comparing one of the larger States of India, noting there are more than 20 states in India with Goa, the smallest State! I dont think Hampi (a tourist town) can possibliy represent the whole of Karnataka.

There are many places to go in Karnataka, some of these are:

Mysore - Mysore Palace, great market
Coorg - coffee plantations
Srevanabelgola (cant spell!) - Huge Jain statute
Ooty (oops, just across to the bordering state of Tamil Nadu)
Gorkana - More serene beaches to Goa
Bangalore - One of India's most cosmopolitan cities, must visit

I hear the temples in Badami are worth seeing too

if you want to go to Hampi, you can take a train from Goa to Hospet (the nearest town to Hampi) and catch a tuk-tuk or bus to Hampi...oR take a private bus...or drive =)

oh yes, train takes about 9 hours

we went to hampi! well worht the visit. Went this february on the train and it takes about 9 hours.

We also went ot dandeli, a town in the state, where we went white water rafting and safari! did this trip through day tripper, http://www.daytrippergoa.com Its well wort it to! you get to see some nice countryside and go white water ratfing. But if you dont want to do this, they take you on a walk around a village instead! WE drove there and it toke about 4hours i tihnk, its not far from the boarder.

Once did a trip with Daytripper, overnight sleeper to Bangalore, picked up a car & driver there visited Mysore, Coorg County, & finished up in Mangalore where he got the train back up to Goa Fabulous trip , it included a night at a game reserve, loads of wild elephants & lots more Karnataka is more the real India, lots of Bullock carts & outside the cities not a scooter or motorbike to be seen, the trip to Danndelli gives you a flavour for the other India too & only takes a couple of days to do. It's well worth the effort to see outside of Goa if you get the chance

I drove through Karnataka on a Pulsar 150 (motorbike), it was a lovely trip but I'd probably recommend a different bike with a more comfortable seat. I drove starting in North Goa, directly south down the coast (along the NH17) and stopping off in Gokarna for the night on the way down and again on the way up... I went as far as Kerela (just over the boarder) and it was a lovely trip and you get to see the changing sights and sounds, definately worth a go if you ride a bike (good thing about Karnataka is that you don't have to wear a helmet, which is a godsend as it allows the wind through your hair.