Is it necessary to buy advance tickets to Park Guell and La Sagrada Familia? We are on a pretty tight timeline and don't want to spend my vacation waiting in line to purchase tickets.
Most definitely for both.
If you want the full on Modernist Architecture day then also include the Palau de la Musica Catalana
1000 Palau de la Musica Catalana http://www.palaumusica.cat/en/the-art-nouveau-building_23602
1200 La Sagrada Familia http://www.sagradafamilia.cat/sf-eng/index.php
1500 Park Guell http://www.parkguell.cat/en
I don't know about Park Guell but I would definitely buy an advance ticket for La Sagrada Familia. It's absolutely beautiful, there's so much to take in. I was there for a couple of hours but felt like I hadn't seen everything, I will go back there again someday.