Dancebert,
It's great that you will be spending 6 nights in Sevilla as there is so much to see & do there.
The only tickets you might want to get a day or 2 before, would be for a flamenco show.
We chose to go to 'Casa de Flamenco', recommended by RS Spain book.
This show is only an hour long & does not include a meal nor drinks, but it's quite worth it.
We didn't book tickets in advance & the line was not long when we visited The Royal Alcazar this past October. We were actually there on a Monday & were treated to s free entry between 4- 5PM.
However, you may want to buy your tickets online to skip the line:
http://www.alcazarsevilla.org.
If you find a long line to buy tickets for the cathedral, you can buy your combo tickets at the Iglesia del Salvador ( Church of the Savior) where there's usually no line, then visit the cathedral afterwards by skipping the line.
On Plaza del Salvador, where the church by the same name is located, there's a great tapas bar, 'La Antigua Bodeguita', with outdoor seating. You'll see it right across from the church, there are small round tables with high stools & white umbrellas.
It's a very popular with the locals & it may be crowded, especially on the weekend.
Don't confuse this tapas bar with the one next door.
We ate lunch there 3 days in a row!
Make sure you visit Triana during your visit!
Enjoy Sevilla!