On the indy track do not brake going into corners, keep the accellerator full on and shift down to third at the braking zone and turn in, taking the inside line, you'll fly past everyone by the second straight and should finish the race a good 6-8 seconds ahead.
The next three races are just high speed dodgems. Don't brake going into any corners if there's a piece of "mobile armco" you can use instead. If you try to race clean the AI will just ram you off the track so strike first.
If you gold the first 4 races just quit and take the crown. Daytona is next to impossible, the slightest tap will send you flying off the track and your opponents are all much faster than you, invincible and can draft you from half a lap back.