The MotoGP circuit travels throughout the world. I was in Spain during the MotoGP that took place close to Jerez that is just about an hours drive from Seville so we decided to go.
It is worth staying a few nights in Seville to experience the city. The drive from Seville is beautiful as you drive throughout the countryside + you will see a number of motorcycles on the road headed to the race.
Once at the course you can walk around the grounds which have great views of the track and also purchase tickets to sit in the stands (I believe you have to purchase all tickets prior to the race day).
The race itself is such a thrill. Watching the bikes zoom by and then practically lying on the ground to make the turns, is incredible. They do about 26 laps around the course, which goes by quickly.
Definitely worth going to see a race like this to experience a new city.