I did about 1800 miles in 4 days last summer, as well as some 1000 mile weekends. You have to be quite selective in what to pack. Look up your route to see where the nearest dealers are, just in case. I haven't been stranded or had any major problems. Work your way up in endurance before you do the big trip. Once you get adapted to the seat, etc., you'll do fine. I think the S3 is most comfortable cruising at around 70. Any extended time above 80 can get fatiguing (but it's still fun). Don't try to do the biggest chunk of miles the first day. Wear good gear, and try to avoid anything that flaps around, since being unprotected from the wind, all wind-related effects are exaggerated. If you are nearing a tire change before you go, you might consider doing the Pilot Road 2, as they will give better wear than the Pilot Power, but still have good side traction for any twisties you encounter.
BTW, I am planning some trips this summer. 3000-4000 miles to Colorado and back early June, 1000 mile RAT weekend June 20-22, hopefully something in July, probably another 2000 miles in four days in August, another 1000+ mile RAT weekend to Bend, OR in September, plus another 3 or 4 track days. Yes, Matilda, Dreams do come true.
Naked, naked, naked!
Unflappably Nonchalant, with some exceptions