Sarasota/Bradenton International Airport is about 15 minutes from the school. Tampa International Airport is about an hour away. Tickets into TPA are generally $100 or so cheaper than SRQ. There are shuttle services that will take you from the airport to your hotel in Sarasota/Bradenton. Keep in mind that rental car companies charge $25-35/day extra for people under 25 (this is on top of the regular fare and is usually not added until you pick the car up, so if you book online, beware of this).
When you visit the school make sure you check out south Lakewood Ranch and Sarasota. There is not much around the school yet, and Bradenton itself blows IMO. You just gotta head 5 minutes south. From school, go down Lakewood Ranch Blvd. to University and turn right. You will then be in Sarasota. Driving down University, the first light will be Market Street. On the right behind the shopping center is Colonial Grand, the most popular apartment complex for students. As you continue down University, you will pass The Tuscany on your left (Medici Court) and Palm Aire on your right (Whitfield Ave), two more popular complexes. Continue on University to US41/Tamiami Trail (10 minutes, you will pass SRQ), and turn left on 41. At this corner is the world-famous Ringling Museum (big pink building). Follow 41 south and you will approach downtown on the left. Take a right on Gulfstream Ave (Ritz Carlton on right) and you will cross the Ringling Bridge over Sarasota Bay. This will take you to St Armands Circle, filled with restaurants and shops. As you walk the circle, follow the sign to Lido Beach, which is a 2 minute walk away. When you go back over the Ringling Bridge on your way back, after you take a left back onto 41, take a right onto Main Street and check out downtown.
This is the best way to experience the area.
By the way, Lido is the smallest of the area beaches but I've included it because of its accessibilty and proximity to St Armands. If you want to see the nicest beach in the area, and the #2 ranked beach in the country, go to Siesta Beach. To get there, take 41 south to Siesta Drive and turn right. Follow the signs.