There are airports serving Trieste (an hour north of it) and Brindisi (north of Otranto). So, if you really are driving the whole Adriatic coast, fly into one and out of the other. If those are expensive, look at the next closest airports (Venice instead of Trieste, and Bari instead of Brindisi).
As for flight prices, there is no rhyme or reason any more - you just have to check for your dates and home airport.
I agree with acraven - first decide what you really have time to see. In 8 days, there's no way you can see more a tiny fraction of the places between Trieste and Otranto. Then decide on which airports are most convenient for the area you want to see, then check prices and see if you need to modify the airports to get a better deal, taking into account how much you'll spend in time and inconvenience to get from the "cheap" airport to where you want to be. For instance, if it's "cheaper" to fly round trip to Rome, how much time and money will you spend getting from Rome to Trieste and from Otranto back to Rome? With only 8 days, that probably won't work well.